What should I do and see while i'm in Los Angeles and Ojai, California?

I dunno… the La Brea tar pits? There’s an open pit of tar just sitting there middle of LA, with fake mastodons and an adjacent museum of natural history. They’re only now considering to stop LA oil drilling.

Sometimes you can go see whales, though it may be pricey and I don't know your budget.

If you eat meat you should consider trying the famous In'n'Out Burger fast food chain which is native to southern California. Definitely get some fries with it if you do (though unlike McDonalds their fry quality can really vary throughout the day from good to kind of dry). Nothing iconically vegan here that I'm aware of in a way that people from other states lust after and know about.

There's celebrity and Hollywood stuff to see of course, the citywalk with all the celebrity stars in the sidewalk, the Chinese theater, some museums for that. Universal Studios theme park has a vehicle tour thing which is mostly gimmick and does require paid admission to the park, I wouldn't place it high on my list unless you had a lot of time (no visits to anything but held over preserved old sets and some theme-park-ride gimmicks along with trivia but it's not uninteresting if you have an interest in older universal movies). There are also other studio tours which are a bit more authentic and involve getting close to the sound-stages which you can check into but many of them require more advanced bookings and may be more expensive.

Without knowing a budget and how much time you have to spend it's hard to begin. LA has a lot of interesting things, say Griffith Park Observatory which is pretty famous and which has amazing views of the city after dark. Though note you may have to take a tram/bus up to the top or walk a little ways, it's not a super quick stop but you can probably quickly see the outside, take some photos and leave within an hour.

There's also the Getty museum which has some pretty interesting artwork by a number of famous masters. Admission is free and you get to take a tram up to it but you must book a reservation in advance for a time-slot.