I tried to read a couple of descriptive threads about the summons themselves, but sadly I couldn't find it anywhere. As far as I am aware, they were first used in the series by The 3rd Hokage. I know that the summon relies heavily on speed and utility. Being an animal which is very much alike humans, I would believe they have strength in utility and resilience in terms of using them. There is also that scene where Enma turned into a staff which was powerful enough to push away the nine tails, or aid Hiruzen in beating the other 2 hokage, so strength also has to be a strong characteristic. This is about as far as I know.
@Slacker