It shouldn't need oiling then.
Assuming the machine has had a good chance to warm up inside, here's what I'd try. Unthread the machine and take the needle out, leave the foot up, and run it at full throttle for 3 minutes with the straight stitch. Give it 10 minutes to rest. Then turn it to the zigzag stitch setting and run it for another 3 minutes at full throttle. Let it rest. This may "burn off" any oil or lubricant that has become gummy during storage. (I recommend taking the needle out to make sure it doesn't hit something and break while you are running the machine fast like this.)
When you rethread to try again, be sure to clean the bobbin area of any lint that may be stuck in there. Depending on the machine, this may require unscrewing the plate that covers the feed dogs so you can get stuff out.
I would also take out the entire bobbin assembly and clean that area. Put a drop of oil on your finger and run it around the outside of the bobbin race (the thing that holds the bobbin case, has a sharp finger on it) before replacing. If you've never done this before, be sure you have the manual to help you with this; otherwise you may not be able to get the bobbin assembly back in. I've done it so many times it's no problem, but it's confusing if you are not familiar with this assembly.
If all that doesn't work, I'd take it in for servicing.