Yes
about 3 days with rests
22
No! Ca has NO authority to enforce an inspection requirement from TX. It can however enforce the registration, if that has expired.
24 hours
The drive to NYC is longer.
yes, sales tax will depend on whether or not you actually live in Texas. If you do not and have no plans on registering the car in TX, then no sales tax. If you live here, but are keeping your CA residency, then yes, you will have to pay the tax.
It is an 18 hour drive covering 1,277 miles.
About 1500 miles, so it will take you about 20 to 22 hours to drive.
Google Maps estimates the driving time as 24 hours,
The shortest driving time is 25 hours.
The driving distance between Oakland, CA and Odessa, TX is about 1,450 miles, so you'll probably need to spend the night somewhere on the way there. The drive time itself is about a day. Be careful about when you drive through Los Angeles, though, as traffic through there and Riverside can add hours to this time.
It is 1,692 miles according to Google Maps.