see also System.Data.OracleClient namespace discontinued?
(Firstly don’t panic yet, System.Data.OracleClient is not being removed by Microsoft yet, however it is not
There's a big difference between being deprecated and being removed.
If you're just using the subset of functionality that is common to both SQL Server and Oracle, then you should be fine moving through to ASP.Net 4.0 and continuing to program how you do currently.
Using something like EntitySpaces, would let you be relatively provider-agnostic. (it uses OracleClient in it's DAL)
Completely agree with Philippe about Oracle's client software being a pain. I've lost track of the number of times I've installed it and hated the experience. Give me MySQL, SQLServer or even Access in preference.
(Actually, I take back the Access comment) :-)