I would guess that you are using too high a gear for your riding. Usually that's when the knees start to hurt. Try lower gears but spinning the pedals faster, and make sure you are shifting down far enough on your hills. Also, each day you will feel a little differently on the bike, some days are always stronger than others. Listen to your legs and if you are feeling not as strong one day, just spin easily rather than trying to keep up with the speed that you rode the day before.
Another thought is to make sure you are not twisting anything as you pedal, make sure your stroke is straight down (actually circular, forward-down-back-up) and that there is no side-to-side pressure on your knees.
Knees are often very sensitive, so be sure not to push too hard when they hurt, they are easily injured. It may be a good idea to spread out your biking days more, i.e. bike 2 days, take a rest day, then bike another day, take another rest day. That gives your muscles time to recover so that they will better suport your joints.
Those are just some ideas, if I think of anything else, I'll pass it along.
Ok! Good hints! I do tend to sort of wobble side-to-side and I think my knees wobble too.
I'll try resting over the weekend and see how that works.