Hi,
I know your question was posted a month ago, but I figured I would venture a reply anyway.
I've seen some interesting studies that suggest lactic acid may have beneficial effects on joints. I've anecdotally experienced this effect during weight training. If you pick lifts which involve the joints in question and use fairly light weights (think in the range of 50% of your 1 RM) then perform high rep sets, this will illicit the "burn" which many people are familiar with. The burn is actually lactic acid build up.
If you are already weight training, then that is good because it can strengthen bones and joints anyway. But if not, then you probably won't be aware of what sort of load to use and which lifts to perform. This will depend on the joints in question. For example, with knees, I would recommend front squats or back squats, but if you are not familiar with those lifts then that would probably be a bad idea, since bad form could lead to more injury. In that case, stick to leg extensions. I would not use the leg press.
For intensive rehab purposes, I would do 3 sets of 25 reps for one week, 2 sets of 20 reps for another week, and then 2 sets of 15 reps for two weeks. You should do this three times each week. Gradually increase the weight each week, being sure that you can still perform all reps. You do not want to go to failure, that will have no beneficial impact on your joints and won't do anything for muscle growth either. By the end of the four week period, move on to 1 set of 10 reps for two weeks and increase the weight further, continuing to work out three times a week. Pay close attention to how the joints in question feel. If there is significant pain still, then do not continue to increase the weight. Stay away from weights in the 5 rep range.
For every exercise you do, take them all nice and slow. If you can not do the lift slowly, then you are using too much weight. Moving fast is great when you are trying to develop explosive strength, but the purpose in this case is to rehab your joints. So go slow and focus on good form.
If you are already weight training, I would drop back to lighter loads as recommended above. You don't really want to be using heavier loads when your joints are in pain, as this will likely prevent them from healing. Yes, heavy weight training does strengthen _healthy_ joints but it won't help an injured joint.
For your shoulder and elbow problems, I would try high rep curls and high rep lateral raises. You might be tempted to do overhead pressing for the shoulders but I would not recommend that for a couple reasons. First, it is difficult to maintain proper form during high rep overhead pressing, which could lead to further joint injury. Second, it is easy to hit failure doing this, which could result in serious injury from dropping the bar on your head, hitting your chin when going upward, etc etc.