I've seen a ton of Shakespeare, good and bad, a fair amount unconventional, but very little I would say was outright "weird". I did see Vanessa Redgrave play Prospero in a TEMPEST at the Globe Theatre in London. She made a rather phlegmatic Prospero and the production didn't really work with a strange mideastern concept. The most interesting part of the production was one of the clowns was sick (Trinculo?) and the Artistic Director of the theatre, Mark Rylance, came in to do the role, obstentibly on book, but he never referred to the script and was very good.
I also saw a Mafioso MUCH ADO which also interpolated some Cole Porter songs in it. It was a hash of a concept that didn't work at all, was badly directed, and not particularly well-performed. Benedick came off like a pouting Shirley Temple.
The weirdest Shakespeare I ever saw was an AS YOU LIKE IT where the forest of Arden became a Circus. One character became an organ-grinder's monkey. There was a two-headed lady, a bearded lady. Stilt-walker. Jacques was a clown. Rosiland at one point sang SEND IN THE CLOWNS. It was, once again, a case of trying to shoe-horn a concept onto a play where it didn't work. It would fall into my "bad" category.
Back in 2007, I played Claudius in a sort of bleak, repressive, facist state, modern dress, multi-media Hamlet. The concept worked pretty well and the play got a spread in AMERICAN THEATRE magazine.