Why Venomancer is played as a support?

The thing is, most of what you can do is just as effective even if you have almost no items at all. While Orb of Venom and Sange and Yasha do provide even more slow, their effectiveness pales compared to what you can do simply with your base abilities.
That's why Venomancer is played as a support - not because he isn't powerful with items, but because he's still incredibly powerful without them. You're better off letting the farm go to a hero who actually needs items to be powerful, because you can get by just fine without them. Unless you're picking carry Venomancer specifically to counter a certain hero (for example 1v1 mid against Templar Assassin), running Venomancer as a carry simply isn't an efficient use of your team's farm.

As for how to play Venomancer as a support, you play him pretty similarly to the way you play carry Venomancer except that you spend more time fighting and less time farming. Use your Poison Sting and wards to harass your enemies in the lane, and use your slow from Venomous Gale to set up kills. Later on, use your wards to push towers or defend against enemy pushes.

The main difference to your play style is that you'll be a little more fragile since you probably won't have as many tank items (although it sounds like you don't build many anyway), so you might need to play a little more cautiously. Otherwise, he's not very different.

The reason why most people don't see Venomancer as a strong Semi-Carry or Carry at all is because he is not. In terms of damage potential and late-game strength every real carry will stomp him. That's a fact.

What Venomancer is strong at however is pushing fast and pushing hard thanks to the power of his wards. He makes a good Suicide Initiator who jumps into the enemy team absorbs as much spells and damage and dies after using his own spells. He also has great damage over time and slows in his arsenal.

Quick Guide to Venomancer

Starting items

Animal Courier/Observer Ward (only one or the other), Tango, Clarity and Orb of Venom (be quick in lane to grab it from the sideshop)

First skill point goes into Poison Sting 

From the first second on you want to harass your opponent as much as possible. Poison Sting + Orb of Venom will make all your attacks deal quite a bit of damage and you don't even get the aggro from creeps if you do it right!

The second skill point goes into Venomous Gale 

Now you start looking for opportunities, if the enemy is low enough you Venomous Gale them, keep attacking and with the help of your ally you should be able to score easy kills, thanks to your early harass and damage over time.

Now for farming

In pub scenarios you will often find yourself just harassing and leeching experience from lane, whereas in higher skill brackets you can go and stack the small camp and do pulls to get some extra gold and experience.

The first item you buy are Boots of Speed, then a Flying Courier, however if you don't have Boots of Speed by 5min then buy the courier first. Optimally you have the boots and enough gold for courier by 3min.

The skill build already starts to vary depending on how it goes. With lvl3 you always want to take Plague Wards so you can keep a look out or try to get some extra damage in when you go for a gank.

If you are forced to play defensively than leveling up Plague Wards further is your best bet, you can jungle quite effectively at lvl4 with 2points in Plague Wards and pushing becomes easy at lvl5. If your ganks are working out then I would level up Poison Sting and Venomous Gale equally, get the second point in  Venomous Gale first for additional damage over time.

After buying boots you want to purchase an Urn, this will give you necessary mana regen, health regen and additional damage over time.

At lvl 5 your build is either 1/1/3/0 or 2/2/1/0, you take your ultimate at lvl6, finish Plague Wards at lvl7 or you put points into Venomous Gale and Poison Sting to level them up equally. If you decided to choose Plague Wards then you want to start pushing, start with your lane and kill the tower, then move on to the next lane, etc. If you went for the Poison Build then always carry a Town Portal Scroll with you past 10 min so you can quickly react to a gank on another lane and help out, hopefully scoring multiple kills in return.

With the mid game arriving you want to purchase Arcane Boots to extend your mana pool and because it's your duty as support (kind of). I would buy wards once every ten minutes because each ward lasts for 7 min. so you can easily just split it to cover the entire ten minutes and then it doesn't really hurt your wallet that much.

After completing Arcane Boots you have several options

You can buy a Blink Dagger or Force Staff if your team needs an initiator and to be more mobile yourself, you can buy Veil of Discord for some life regen and increased magical damage, which if used right increases your damage more than Aghanim's Scepter or you can buy an Aghanim's Scepter to power-up your Poison Nova and gain more survivability.

As the game continues to go on you want to finish up your skill build by maxing Poison Sting after Plague Wards and Venomous Gale last for the Pushing build, and for the Poison Build you finish Plague Wards last.

Now you move on to luxury items that you want to purchase as the game continues to go on

Shiva's Guard is the perfect choice to increase your slow effectiveness, but only purchase it when nobody else is buying one. Eye of Skadi is the best upgrade for Orb of Venom as the minimal slow and damage don't matter, the stats will greatly increase your damage, health pool and the Orb effect is just right. Lastly you want to buy a Butterfly to become extremely hard to take down (given your opponent doesn't have Monkey King Bar already) or you want to build Necronomicon for better push, you can also buy Black King Bar or Ghost Scepter if you need to counter your opponents.

What you get in the end is a monster of support, you have helped your team out so far, not stealing farm from lane by farming the jungle and ancients with wards, you kept at least 1 sentry ward up all the time and you helped push and take down enemies. But you are also extremely tanky and have great slows. Your damage is lower than that of a carry but because of all your slows it's incredibly hard for enemies to take you down and your ultimate can easily destroy them if they don't have  Black King Bar.

Optimal items build

Shiva's Guard, Eye of Skadi, Butterfly, Aghanim's Scepter/Veil of Discord, Boots of Travel, Blink Dagger/Force Staff