hmm, three of them are same meaning as you know, but, when you make a sentance, the person who listen to you feel different.
those are not honorific form, so it would like to use friend or younger people. or rarely , really really close little bit older people who accpet you use that form.
anyway, "봤어?" is usually to friend and younger people. i think it is common expression btw friends, but not to close( not all the times, people who are close can use this too,)
"봤냐?" is usually used btw close friends and famillar friends. it is really hard to use to older person. i couldnt see younger person use this to older person. if someone listen to this form when they are not familliar with, the person who listen might be uncomfortable and think he is rude.
the last one, "봤니?" is usually used from older person to younger person. maybe "봤냐?' make person who listen feel bad, "봤니" make the person feel that person who speak is kind.(this is my opinion 'cuase i like it.)
i dnot know you like this answer, and sorry for pool explanation :( hope u understand : )