I adore this show and I am always kind of surprised that I like it. The Donny Osmond tour came through Chicago when I was a teenager in the 90's and I thought it was the coolest thing ever, especially the remix at the end. To me, the show epitomized the fun, zany side of performing arts.
When the OP says that it feels random and that nothing make sense in the show, are you aware that every song intentionally has a different style to it, and each of those styles is intentionally campy and silly? The Elvis song, the French song, the calypso song, etc. And the story is a Bible story, so it's not random in that it does follow the story faithfully--pun intended.
But I freely admit that if I didn't fall in love with it as a 15 year old theater nerd who wanted nothing more than to jump on onstage and dance and sing Go Go Go Joseph, I definitely would not give it a chance now.