I recently finished a CoS campaign with a small, somewhat oddly-built party. As a module, Curse of Strahd does a pretty good job of keeping the pressure on with very little work from the DM. It's fairly easy to tweak encounters, although as a warning it is also not too hard for the PCs to wander off-track and bite off more than they can chew!
Aarakocra and Flying Players
For your specific example, I think Barovia is a fairly safe place to have a player be an Aarakocra. There are a lot of things you can bring in to make things easier.
A lot of the valley is forested, and the forests are described as incredibly dense, twisted, dark, and foggy. Flying in there would likely be difficult if not impossible.
The forests are also, like everything else in the valley, an extension of Strahd's will: if it's narratively useful for the trees to claw our Birdman from the sky, they could.
As a side portion of terrain, there are a lot of indoor scenes where flying wouldn't put you meaningfully out of reach.
Flying may not put you out of reach of your foes here. While some humanoids might not have a ranged weapon it would be easy enough to add one, and additionally, this is gothic horror with a vampire baddie. There are quite literally endless bats.
Perhaps more dangerously, Strahd and Bucephalus can fly as well.
There is also the Roc of Mount Ghakis, which I had planned to have chase any PC that got too high up. I viewed this "Fly too high, attract the big fish" mechanic as a way to prevent reprisal-free fireballs from 200' by a flying sorcerer.
Barovia's weather is miserable. It's always overcast, often rainy, and storms are common. Flying in a rainy windstorm sounds like a great way to let the DM move you every turn. Lightning is a very real thing that I'd totally have intersect with a 150 lb chainmail-wearing bird on its way to the ground.
But really, the number one in my mind is: unless this is formal AL play (since they ban L1 Aarakocra anyways), don't worry about it too much! As this excellent answer on flying PCs explains, it is often a self-limiting feature that you as the DM should be aware of, but not worried about.
General Class Balance
I had a party of largely Unearthed Arcana multiclasses, and found it balanced out pretty well. Honestly, for a group going into a campaign with a known vampire big bad in it, they went pretty light on the Divine magic.
With one exception (see spoiler), I didn't see any combo in-game or during spitballing sessions with my players that would seriously de-fang anything in the game. Be sure to pay attention to action economy and estimated encounter difficulty, and you should be fine.
The one exception: Strahd himself. The climactic fight is written to be largely party-vs-Strahd. He's relatively tough and hits hard, but he's losing in action economy and the Sunsword will remove a lot of powers and cause him serious harm.
I found you need to play him very carefully and very smart. But remember: he's a master strategist and has been spying on the party via his animal and human servants, and with Scry.