Boy, I wish the deer found ivy (I assume you mean English ivy, Hedera helix) appealing here!! Ivy is a noxious weed in the PNW and is everywhere!! As many deer as there are in the area, I would have hoped they might put a dent in it but they don't seem to bother it at all. Probably too many other goodies for them to munch on :-)

You could try Grass-B-Gone on the crabgrass. It is a weed killer that only targets grass-type plants and won't bother the ivy at all. And yes, the ivy should overwhelm just about everything else once it gets growing again. About the only thing that grows through an ivy bed here is horsetails and blackberries. Of the three, I'm not sure which is the worst :-)

Ivy is invasive here in the Hudson Valley, New York, too but in this particular location - an island with several tall locust trees whose trunks it climbs - it worked well. Thanks for the suggestion of grass-b-gone.