There are several crossovers, but note...
As it is, yes, there are ways to mix "templates", but these are very restricted.
(Please note that I am mostly interred in the 20th Anniversary editions)
For Garou, there are very few options. One is an Abomination. If a vampire is sick (or insane) enough to try to Embrace a werewolf, the Garou must roll their Gnosis, diff. 6. If they succeed, they die a quick and painless death, courtesy of Gaia's grace. If they fail, they die a long, painful death. If they botch, they rise as an undead monstrosity. They gain all the powers and weaknesses appropriate to their clan, generation, etc.
However, they lose access to all Gifts and Rites that are not related to the Wyrm, and they can never raise their Gnosis trait any higher. Instead of using Humanity/Path, they use their Gnosis to calculate the same things, but if they fall below 7, they enter permanent Harano, and if they lose all their Gnosis, they basically enter wassail.
Other Fera have different effects, like the Kitsune who greet their prospective sire with an intense pillar of flame as soon as vitae touches their lips, the Ratkin who simply keep rotting until they can't move, Rokea lose all their Gnosis instantly and the Corax simply burst into flames at the next sunrise (even if they were theoretically a mile underground).
Referring to your question about Awakened Garou, no. White Wolf has made it clear that since a Garou are half flesh, half beast spirit, the Avatar of a Mage could not awaken in a Garou. Kinfolk can, however they are a minority within a minority.
Awakened Mages simply become normal vampires, as the Embrace shatters a Mage's Avatar. Sorcerers are the same, except that the ST may rule that your hedge sorcery paths or Numina become certain dots of Disciplines or Thaumaturgy/Necromancy, etc.
Wraiths have no bodies and therefore cannot be Embraced, and since they are not living, they cannot Awaken either.
Demons are very different from all the other splats. They are the primordial, spiritual beings who aided in the creation of all of Existence. They can possess a body like that of a Mage or Imbued, but this is the only way one of those beings could ever use Demon Lores, and in that situation they aren't themselves, the Demon has complete control of them. The Lores are powers inherent to these former servants of God, and as such are wholly exclusive to them.
Kindred are likewise very exclusive, HOWEVER. In V:TDA: Wolves of the Sea supplement, there is a new Knowledge called Rune-Lore and a new Merit called "Rune-Wise". With Rune-Wise, a character may, through their mastery of runic knowledge, buy hedge sorcery paths from the WoD: Sorcerer supplement at their normal cost, but only up to your number of dots in Rune-Lore.
Other instances are the thin-bloods. In Times of Thin Blood, it is stated that some thin-bloods and generally all dhampir can do the same, except they don't have to use a runic methodology to their magic, but rather use the limited power inherent in their weak vitae to use it.
As for Garou Gifts, kind of. Through the use of Fomor from W:TA: Freak Legion - Player's Guide to Fomori, a Kindred could achieve the power to use Garou Gifts.