[cypher]

It's not that uncommon for hamsters to have problems with the teeth like this, I had one & opted for having the teeth clipped regularly & he did just fine.
None of the options are risk free, the teeth can be clipped without anaesthetic once your ham is used to being handled but that does run a risk of teeth splitting or roots being damaged, burring is safer but the anaesthetic carries a risk when needed that frequently. As souffle said the teeth can be removed but that also carries risks so not the easiest choice to have to make.
If the teeth are removed they can still manage some hard food as they can break it down with their molars so shouldn't need a totally soft diet.
Teeth grow a bit slower in winter so clipping or burring usually only needs to be done about every three weeks & about every two in summer.
If the teeth have pierced the palate that will take time to heal so your ham will probably need soft food for a little while but with regular trimming or clipping they can manage a normal diet.