Would a 4870 512m card be able to run a 24" monitor with no problems or would it be strained at default resolution 1900 x 1200? Upgrading from a 7800GTX which is getting strained. Or would the 4870 X2 be better for this?

It would depend on the game, really. The 4870 would be a huge improvement over the 7800GTX, that's for certain, but at 1920x1200 the 4870 may still have issues with some games, namely Crysis. But for the vast bulk of other current and upcoming titles, it should actually be sufficient.

I have the 4870, it can pretty much play anything you throw at it in 1900*1200 except crysis. I play it at 1600*1080 high settings and get average 25 fps.

acknowldged georgy, thanks nottheking