I’m completely stumped here.
Theories, anyone?
Gourd is a long-used reference to one’s head. (Thick shell/skin around a soft center.)
Stoned meant drunk in the 1950s, but shifted over to the drug culture in the late 1960s. It is not exactly clear where stone/stoned became “drunk” or “high” but the (unattested) speculation is that it was a back-formation from phrases such as stone crazy. In that usage, it was simply an intensifier meaning “completely” (e.g., stone broke) (see the Word Maven - stone, adjective. It appears to have first been used in “stone drunk” and then the “drunk” was dropped, leaving “stone” as the meaningful word.
So “stoned out of one’s gourd” simply means to be so drunk or high as to be out of one’s head.