More to the point, what does "surry" mean? At
it sounds as if that really is what they're singing. How you spell it I have no idea, but a number of lyric sites do seem to go for "surry" (not that I really trust lyric sites to get spellings correct).
Anyway, back to "stoned soul picnic"... as far as I know (which may be not much) this means nothing more than the sum of its parts:
"stoned" = under the influence of recreational drugs
"soul" = to do with soul music (and/or various other aspects of black American culture)
"picnic" = outdoor event or party
So, it basically sounds like some sort of outdoor get-together where there's soul music, drinking and drug-taking going on.