Acharei Mot - Sh'vi'i
The Torah Says No.
Homosexual relations between men are forbidden in no uncertain terms. (This is meant not to permit lesbian activity, it's just not discussed here.) Bestiality is expressly forbidden to both men and women.
The sexual practices that G-d has forbidden were performed by the Canaanite nations. It's for things like this that He's driving those nations out of the land. All of these forbidden relationships carry the penalty of kareis.