Jen, have you ever tried improving the soil? I plant under oak trees in my woodland ravine garden and have no such problems. Oaks are 'usually' fairly deep rooted and relatively good to garden under.

As long as they get enough sun and are not shaded out by the oak trees the following grasses do well for me in difficult (ie,very dry) spots.

Panicum spp.
Andropogon gerardii (big blue stem)
Schizachyrium scoparium (little blue stem) - there are some lovely cultivars.
Chasmanthium latifolium (northern sea oats)
Eragrostis spp. (weeping love grasses)
Sporobolis heterolepis

If it is shady you might try some Luzula spp.

note: you will have to water these in the first year to get them established.
a.