I have had the achilles thing. About two weeks into a trip both achiles started hurting really bad after about 10 mins of riding. No rhyme or reason, I had ridden thousands of miles and was in good shape. After about an hour it would go away.
I was too far removed from anywhere to do anything, so since it wasn't life-threatening I just pushed through it. Really painful though, but it did eventually get better after about a week and a half. I kept them warm all the time and tried to stretch before getting on the bike.
As for the knee- I wouldn't keep riding for that, you might do permanent damage. I've had knee issues too that resulted from using pedals with too much lateral play. I switched to Dura Ace style locked in tight and never had another issue. That was road cycling though.
Did you switch pedals or something? Have you tried a shim for either leg (it sounds like one leg may be shorter than the other, which is pretty common)?