20 nests will probably trigger their next upgrade, but you should be fine. Focus on getting oil and flamethrower turrets, which can defend against the highest levels of biter evolution. In addition to DaveMcW's answer, it also depends heavily on the size of the nests (in terms of number of spawners...

I'm kind of cramped in my current base and am looking to expand outwards. I need to clear biters nest on the map to safely expand but I'm worried about that by killing them I'm making them stronger. How much of a thing is that? Can I get away with wiping out 20 nests without having them making evolu...