
link for Jamie's suggestion:
Elfin

Just throwing this out there, some parts match, others not so much:
Some Small Magic

You're welcome! Happy to help. I'll move this to solved for you.

Kind of sounds like
Dying to Know You, but not all the details match.
Confessions of a Teenage Baboon or something else by
Paul Zindel? He grew up in Staten Island and most of his books are set in and around that area, and mostly feature disaffected youth.

Perhaps:
Sands -- seems to have both a desert setting and giant birds that are ridden upon.

Yay! Happy to help. Here is the link for your book:
A Question of Happiness

Yes, Randy has some very weird stuff with an isolation tank! Here is the link for:
Head On! Happy to help!

Another possibility is
John Benton -- very similar genre, but his books always had a scene at the very end where the protagonist finds God and repents their sinful ways.

I would guess something by
Jack W. Thomas. I think the one with the gang rape in the van is
Randy but that doesn't fit the rest of the plot you described. All his books were pulpy, exploitative, and grim.

I believe these are the books by
Janine Boissard.
A Matter of Feeling is the one that I remember most from my childhood, but I don't believe that's the one you specifically mentioned. She wrote several books about this family, though.

possibly,
Pantomime?
Caraval for Carly's suggestion - although that is a 2017 publication.

You can ask your public library if they participate in an interlibrary loan program where they can borrow from other libraries outside of your area. Cubby in Wonderland was reprinted in 2001 and there are several libraries that own copies, according to Worldcat.org
The Devil and Winnie Flynn is about the legend of the Jersey Devil.

This is
Escape from Nowhere. The opening line is "Call me Carla," and she goes on to reference Moby Dick.

Margaret, Frances Farnsworth wrote a bunch of stories about adventuring bear cubs, so if Tike & Tiny isn't it, maybe check out her others, such as
Cubby in Wonderland - which I think features just one bear cub and his momma bear.