I think all are in common use.. but "hence" sounds more appropriate.. and "thus" sounds rather old-fashioned... I prefer to use more ''therefore'' than the others.. :)

There's no real difference in the meaning. Example: Yesterday I was sick, so today I cannot go to school. Yesterday I was sick, thus, today I cannot go to school. Yesterday I was sick, hence, today I cannot go to school. Yesterday I was sick, therefore, today I cannot go to school.