How to repair door knob that won't close?

I found that for our main bedroom door, the problem is that the door the latch is in, is about 1/4 to 1/2 inch away from the strike & doorjamb. So that about an 1/8" or so tip of the latch barely sits in the strike. The other problem is, the doorjamb seems to be pushing on the door, so that when you close the door (and you have to kind of REALLY push on it to close for the latch to enter the strike), since the latch isn't all the way in the strike, the counter-force from the doorjamb pushes the door and forces the latch out of the strike causing the door to re-open in a heartbeat.
So.. what to do? I either have to find a doorknob assembly with a longer latch that will rest deeper in the strike or i have to find a way to make the strike sit out further from the doorjamb? Or take the door off the hinges and rework it so it's closer to the strike/ doorjamb? (don't like/think i need to do this last option)
Thanks in advance...
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