Hi Taryn What you want to do will be a significant piece of finish work....here's why:
If you try to cover with an oak veneer, you will really have to remove each tread and riser, sand each down to clean, bear wood, cut the bull-nose off with a table saw, apply your 1/4" luan oak plywood or veneer strips using contact adhesive, route the edges square, then apply a new bull nose using 1 1/2" X 3/4" oak boards held in place with bisquits and glue, then route the edges over with a large quarter round bit, sand and reinstall.
To replace, you'll have to remove each tread and riser and use it for a templet to cut them to eactly replace the old treads and risers.
Depending on the age of your stairs, it will probably be easiest to replace them, as the act of removing them often splits the older, dry wood. Also, contact cement, with continued walking on it, will eventually lose its adhesion.