The Oak Orchard is dam controlled and its headwaters flow through a series of swamps. This helps lessen runoff a bit and it is not as flashy as say the Erie tribs. However, I think they got ALOT of snow in Buffalo yesterday. With the warming temps next week, that snow is going to have to runoff somewhere. The Oak is located north of the snow belt and often gets nothing when buffalo gets clobbered. If it is just the rain monday and tues, you will be ok but the snow melt could be the killer. That said, there are plenty of other places to fish up there. Pretty much every trib that flows into lake ontario gets fish assuming there are sufficient flows. Some of them only have enough water to get fish when everything else is completely blown.
If you are going to postpone, I would postpone until next year. The Oak is fed by the Erie Canal and once the canal is drained at the end of november, flows can get low. The fishing for browns starts to slow in December with many of the fish getting pretty nasty. It can still be ok but I wouldn't drive 8 hours to fish it.
FWIW I was planning on fishing WNY next weekned and I am expecting the places I fish to be completely shot.