Strong champions on 3v3 are champions with:
Just look for champions with those things. Basically a champion that can win their lane, gank effectively, farm well, get around the map and get where they need to be in teamfights will do well. (Note: No champion has everything)
Sċm has a good tier list you can look at.
The best teamcomps consists of Meta (Tanky Melee AD) top, AP carry bottom, and an effective jungle. Top and bottom lane farm and keep their enemies low so jungle ganks are efrective and they have the items from kills / farm to turn teamfights in your favor. Jungle gives map control and ofcourse ganking options. Sometimes having two people bottom to deny their 1 person also works, but a good team will almost always shut this down.
In my eyes, the best way to sum up 3v3 strategy is map control.