Just pull them up - soon, before they seed. Mowing will also keep them in check as will improving the grass so there are no bare patches for weeds to take advantage of.

Looks like Myrsiphyllum asparagoides, Florist's Smilax.

Looks like an air potato to me, latin name escapes me. Dio or Disc-something or other! I know that's very helpful...LOL, it'll make a pretty vine in the house, and eventually make little tubers along the stems so propogation is easy. I don't think it's hardy in your zone, if it were I'd keep it inside, it can be a problem in the south. It may go dormant in the winter even inside. Nothing like Kudzu though. Chaz

i get the same vine growing along the edge of my yard near the ditch. i just cut it back with the mower and spray it with round up. this keeps it in check, but the only way i have ever gotten rid of it was to totally kill off everything in the ditch, but this lead to erosion, so now i spray a low dose to stun and slowly kill back the weeds.