I have a driving license from CT (Connecticut), and a vehicle registered with my name in OR (Oregon).
So Can I drive in OR with my CT Driving License? And for how long I can drive?
You can drive temporarily in any US state with a drivers license from any other US state.
However, if your residence is no longer in CT, then you must get an OR driver's license. You can read about relocating on the OR DOT site, but basically it says if you change your residence, you need to change your address with the DMV.
As long as you are in OR temporarily (there's no good definition for temporarily, so it's mostly up to you) then sure, use your CT license.
You can drive in Oregon with a CT license. That is the easy part.
If you change your state of residence, most states require that you change your license.
Since you have registered your vehicle in Oregon, and not CT, the Oregon DMV (and any police officers you happen to meet) may wonder whether you are really a CT resident.
This may be helpful, too: http://www.oregon.gov/ODOT/DMV/driverid/residency.shtml
From Article 4, Section 1 of the United States Constitution:
Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State.
This means that documents issued in one state will work in any other, including drivers licenses. As others have said, if you move, you'll need to update, but this is the legal justification for why your driver's license, passport, diplomas, unemployment benefits, etc... all work in every state of the Union.