How to counter invisible heroes?

Most of it gets solved by strategy:

• Pushing towers as a group lets you use Sentry Ward to maximum potential. You drop one to watch for heroes like Riki/Nyx Assassin/etc. sneaking up behind you
• Dominate heroes like Riki in lane so they have a shitty start. Riki does not play well from behind.
• Eventually get a Gem, give it to a carry or utility that will be able to hold it without dropping. Then do most things as a team or when you have sight of the invis hero.
• Have your supports work as a duo so it's hard to kill them both as a solo ganker.
• Also, don't let them snowball. That usually means watching positioning and using Town Portal Scroll to help heroes that are getting dove or whatever.

However, in pubs you won't always have that kind of teamplay.

Things brings us to item choice:

Detection

• Dust - is useful when you're playing aggressive. If you see someone like Riki off farming, then you and a few others can group up and gank him with Dust. Otherwise, Dust isn't hugely useful because if Riki initiates on you, then you're already at a bit of a loss. If you're against a hero like Nyx Assassin, it also won't save you because you need to see him coming.
• Sentry Wards - are useful when you're doing stationary things. For instance, if you're pushing their tower, defending one of yours, or doing Roshan, then Sentry Wards are very useful against invis heroes. Otherwise you end up dropping them everywhere which is not very economically viable.
• Gem - is excellent if you either get it early (i.e. you knock out enemy vision and make it hard for invis heroes to gank, which they need to get their early advantage and snowball), or get it when you're ahead (so someone can hold it).

Force Staff

This is one of the most useful support items out there. Let's say Riki smoke clouds you. That disables spells (e.g. Crystal Maiden's Frostbite), but you can still use items. Force Staff yourself out of the cloud, turn on Riki to stun him, then run away or Town Portal to safety.

Mekansm

This helps you win team fights, but it can also help you survive a gank. Let's say Bounty Hunter shows up and gets you with a Jinada proc. You're at half health, but then Mekansm up to almost full. He won't be able to finish you. In addition, you'll also get a lot of bonus armor from Mekansm, which helps a lot against heavy physical damage dealers like Riki, Bounty Hunter, and Nyx Assassin.

Urn of Shadows

While not as useful as the other items above in this situation, it still gives you some HP, a way to heal, and a DoT(Damage over Time) that can fuck up low HP heroes like Bounty Hunter and Riki. Going invis won't stop the DoT.

Medallion

This item gives you bonus armor, which helps a lot against physical dps. In addition, Medallion has a debuff which can help you pick heroes off quickly if you get them locked down. It also helps a lot for doing early Roshan.

Ghost Scepter

Ghost Scepter is an item you'll come to appreciate as a support. Typically you get it after 1-2 core items when you're against high physical damage teams. If Riki Clouds you, you can pop Ghost Scepter and he can't touch you for 4 seconds. However, you will take bonus magic damage, so something like Bounty Hunter's Shuriken Toss will hurt a lot more.

You can also build casual Bracers, but that's really a last resort. Necronomicon can also be useful, but it takes a hella long time to farm and is only useful for pushing/defending (you're not gonna randomly pop Necronomicon to just see if there is an invis hero around).

When late game comes, Scythe of Vyse is by far the most useful item because it forces them to be visable and unable to attack for 3-ish seconds, while also having a basically instant cast time. Heaven's Halberd can situationally be useful because it gives you more HP, Evasion, and you can Disarm. However, Heaven's Halberd is not the best against BKB(Black King Bar)  heroes, as BKB dispells Heaven's Halberd.

Positioning & Map Awareness

Positioning is something you'll have to just get the hang of. When you're team fighting, you don't want to be on the front line as a support, but you also don't want to be so far back that Riki can pick you off before your teammates can react.

Map Awareness is something you need to learn ASAP. If you see Riki  farming on the other side of the map, then it's a good time to go do things like Ward. This is especially true if there are no Towers that he can Town Portal to quickly.

You need to keep track of things you know and don't know. If you see 4 heroes on the map and the 2 in your lane are playing hyper aggressive, then you can usually assume there is an invis hero around and you should back off. Otherwise they're being really dumb and overextending.

Map Control

This is another piece of the puzzle. It applies moreso to non-invis heroes, but is still important nonetheless.

This means mostly having vision of more than they do. This is done with wards, but also by taking down towers and pushing the wave out (i.e. your creeps are on their side giving you vision).

When you have map control, you're more likely to scout out things like a RikiRiki farming, or the point when Nyx Assassin goes invis and is attempting to gank.

On a similar note, if you're actively counter-warding, then it's much harder for the enemy to even know if it's safe to gank you, nor know where you are. Let's say Riki blindly roams your jungle. He spots Crystal Maiden farming some neutrals and springs on her. She pops Dust as soon as she sees that the Huskar farming another nearby camp is responding to her pings. Riki has no idea that he's in for a Huskar Dunk because he has no vision. Even if he gets the Crystal Maiden kill, your Huskar get a higher priority kill (i.e. Enemy Carry kills Allied Support. Allied Mid/Carry kills Enemy Carry).