From the way you describe the condition of your tires, it sounds like you have two bent axles. All it takes is one good hard bump to bend them. If they are Lippert axles then in all likelihood they are bent.
Tubular type axles have a slight bow in them that should be continuous across the whole length of the tube. As the weight is added to the axle tube, it will tend to straighten out to the point were the wheels a basically perpendicular to the road surface. As quick check, park your trailer on a level surface, go to the back of it and have a look at the wheels. The axle tube should be relatively straight and the wheels should look parallel. Also, look at the axles between the springs and the wheels. Each side should be the mirror image of the other. If there is any difference then it's likely that the axles are bent and replacement is the most likely option.
It would be in your best interests to go to a good shop that deals with trailer repairs. They can tell you what the condition of the axles.
As for the tires, replace them now! Any kind of damage on the tire like what you described is not good. When you do replace them, go one load range up for added safety.