Given the recent patch nerfing armor and hitpoints, I no longer strongly recommend this guide. Perhaps it is a testament to the guide as it was written that it's item build was nerfed, but now it is no longer particularly overpowered. That is all.
***END EDIT***

Tankstix 

Tankstix is by far my favorite way to play Fiddlestix. This is my favorite hero to play and my favorite build. This build is not a perfect high-level strategy, in fact it probably only works well at the lower levels of play where I spend my time. Again, I emphasize that this build is intended for low level play and I believe is a good build for beginners who will especially benefit from survivability.

The idea behind Tankstix is to max Drain and Armor/Magic Resist Early-Mid game to basically out-heal any but the best dps. Because it focuses on Drain, this strategy allows Fiddlesticks to jungle effectively during the early game then transition to the battlefield at around 8 minutes. Tankstix focuses on Armor/Magic Resist and Ability Power early game to maximize drain, then tops it off with HP/Ability Power late game to ensure survivability and lethality during Crowstorm. The strategy transitions from fast-paced jungling to a highly-aggressive mid-game to a passive late-game defined by mediocre tanking and an occasional well-timed crowstorm.


Abilities

Dread (Passive)
Nearby enemy champions have their Magic Resist reduced by 16.

Terrify (12.5 seconds)
Strikes a target enemy unit with fear, causing it to flee in terror for 1/1.5/2/2.5/3 second(s).

• Terrify is a good disable, useful for keeping your life drain and ultimate on a target. Against one hero, the Terrify and Drain make you unbeatable early game 1v1.

Drain (12 seconds)
Drains 50 / 75 / 100 / 130 / 160 (+0.4 ability power/s = 2.4 AP scaling) health each second from target unit and gives it to Fiddlesticks.
Lasts up to 6 seconds.

• Drain is the core skill of this build. The entire build is focused on increasing defense enough that drain heals you faster than enemies can kill you. Drain lets you kill creeps efficiently starting at 1 and even solo dragon at level 5. Drain lets you engage opponents 1v1 and end the battle with full health. Drain becomes weaker and weaker late game as opponents build magic resistance and dps, but allows you to dominate the battlefield early-mid game. The weakness of drain is stuns and disables which your best bet is to flee from or time properly to avoid.

Dark Wind (15 seconds)
Strikes an enemy target and then bounces to a nearby enemy unit. Deals 100 (+0.35 ability power per strike) magic damage and silences for 0.75 sec for each strike.
Can bounce up to 3 / 5 / 7 / 9 / 11 times and may strike the same target many times.

• Dark Wind is a high-damage spell against multiple enemies. The bouncing silence on Dark Wind makes it highly valuable for late game team fights. One level of Dark Wind at level 2 is useful for accelerating your jungling process and the silence is good to engage opponents with, but purchasing higher levels is unnecessary until later levels where it dominates team fights.

Crowstorm (150 seconds)
A murder of crows flock wildly around Fiddlesticks for 5 seconds, dealing 150/250/350 (+0.4 ability power per second = 2.0 AP scaling) magic damage each second to all enemy units in the area. This has a 2 second channel duration and teleports Fiddlesticks to target location.

• Crowstorm is the real reason I play Fiddlesticks. Crowstorm is the main reason why Tankstix is a feasible strategy and not just a fun diversion. With Cleanse, your Crowstorm cannot be interrupted during channeling. With the massive defense that Tankstix carries, you probably won't die until the effect ends. Opponents have two options when you blink in with this feathery Armageddon - run or die. Left unchecked, Crowstorm can ravage an entire enemy team. With a bit of planing, Crowstorm can be a double kill every 2 minutes.

Skill Build
1. Drain
2. Dark Wind
3. Drain
4. Terrify
5. Drain
6. Crow Storm
7. Drain
8. Terrify
9. Drain
10. Terrify
11. Crow Storm
12-13 Finish Terrify
14-15 Dark Wind
16 Crow Storm
17. Dark Wind


Items 
It's incredibly difficult to prescribe a single item build. If the enemy team is largely physical dps, you focus on Armor. If they're primarily magic dps, you focus on Magic Resist. If the other team stacks Magic Resist themselves, you'll want a Void Staff. 

Basic item build versus a well-rounded team
1. Doran's Ring
2. Blasting Wand
3. Cloth Armor
4. Mercury's Treads
5. Negatron Cloak
6. Chain Vest
7. Warden's Mail
7. Blasting Wand
8. Abyssal Scepter
9. Sunfire Cape
10. Rylai's Crystal Scepter


Summoner Spells
1. Smite.
2. Cleanse.

Smite lets you jungle in 6 minutes what would otherwise take 7.
Cleanse lets you channel your ultimate even next to a stunning hero.


Masteries
I spec 1/21/8, priority as follows:
1. Improved Smite (Offense Tier 1)
2. Improved Experience Gain (Utility Tier 2)
3. +Armor, +Magic Resist, Dodge%, Reduced Damage, +60 HP

Runes
For Runes, the following is my optimal build for this strategy:
+HP (flat) Quintessences
+dodge seals (Yellow)
+AP Glyphs (Blue)
+HP (flat) Marks (Red)

This highly defensive build makes you a tank in early games. With Doran's ring you easily break 800HP at level 1.


Playing Tankstix

Into the Jungle - Early Game - 1-5
Buy a Doran's Ring at the start. If you have absolutely no runes or masteries, also buy a health potion.
At 1:40, neutral creeps spawn. Initiate the large golem with smite, drain, drain again and it dies. At 2:20 golem is dead, you are level 2 (or close) with 160 gold. Procede to kill every other neutral creep on your side. The time is about 4:30, you have about 650 gold and have just reached level 4. If possible, kill the other team's golem. If not, lane until your golem respawns and then kill it.
As soon as you have 860 gold and are level 5, recall. Buy a blasting wand and then go kill dragon. You need golem buff for this. Engage with smite, dark wind, drain, attack, drain, attack, drain, etc. You can kill dragon solo in 40 seconds with this strategy and do so before 8:00 on the clock. Dragon respawns every 6 minutes so kill him again at 14:00.

Confronting Real Players - Mid Game - 6-13
Hopefully, you've steered clear of any real engagements so far. A tragedy really because Fiddlesticks would have made an excellent harasser had you chosen to spec dark wind and lane. Because you jungled, hopefully the other team isn't ready for what you're about to unleash. With a wand, your ultimate should do about 170 and life drain about 120 damage a second. Find one or two enemy champions who look gankable, and coordinate with the laning player to make your entry with a spectacular double kill. Hopefully from behind terrain, ultimate into the enemy, fear and life drain one of them. (Cleanse here is helpful if you went that). The enemy may escape if your partner isn't very good, but you've sent two champions back to base and can push. 

This is the pattern you want to set for the remainder of the game. Tanksticks is about fear. NEVER enter into a situation where you're likely to die. Thanks to life drain and your ultimate, you want to condition the enemy to run quickly away from your champion any time you appear. Use your ultimate to gank enemies from behind any time they're pushing your turrets. Choose ganking targets who lack a stun or silence if possible, because that really shuts down life drain.

Middle game is when this strategy really shines. By level 10, you have max Drain and are working on raising terrify. You've also begun your efforts to farm armor/MR and ability power. Drain isn't going to get any better for the rest of the game, but at this point if you have a bit of armor you can drain faster than most solo champions can dps for. 

Hoping it never comes to this - Late game - 14+

As you reach level 18 (unless you do so long before your opponents), the strategy shifts into a team-fight support/dps role. Your item build has hopefully reached 2.5k+hp/200armor/150MR or so, and you shift your focus on your remaining 2 item slots to ability power. You are not a real true tank, but you're not the same squishy AP fiddlesticks that many people play. You want to steer the game towards team battles only, where your ultimate really shines. Pop in as the fight begins, and the enemy will either ignore you, focus on you, or run - all are winning situations. If the enemy ignores you because you're not a glass cannon, they're wrong - 400dps to all of them, bouncing silence and a 3 second disable is enough to tear apart an entire team. If the enemy team focuses on you, then you're also doing what this build is meant to do. Terrify one, silence the rest, and pop a lifedrain, healing you for 200dps. You aren't going to stay alive indefinitely, but if the enemy is focused on you, your team's real dps can do their job quite nicely. If the enemy runs, your team will probably get 1-2 kills and can begin your push.


Tankstix Comments

This strategy usually works fairly well at my level of play, but has some weaknesses. First, champions who stun or silence can interrupt life drain which basically counters your entire early/mid game strategy. Skilled players who know how to gank junglers will counter the early game strategy.

- Choose your fights well - If you focus on Armor, aim to engage enemies with physical dps. If you spec MR, engage casters primarily.

- Play mind games. If you score a solid double kill at level 6, you begin the route to being feared. Engage their dps as early as you buy decent defense and make them realize that they can't kill you as long as you life drain. Basically, make the enemy realize that running from you is always their best option and that conditioning will carry over to late game where enemies will overjudge your abilities and your survivability.

- Kill Neutral Creeps. Make sure you always have a Golem Buff - the mana regen means you don't ever have to buy ANY mana/mana regen items. Every time dragon is up and your ultimate is on cooldown - kill him.

- Drain Creeps - Without Dark Wind, you're getting fewer creep kills and therefore less gold than other Fiddlesticks builds. By level 9 with golem buff you can Drain every 9 seconds for a kill almost every time, plus it keeps your health topped off. Just don't Drain if an enemy engagement is imminent.