Hitch a ride = you're going on get a ride from someone. Take a ride = is used when you're offering to drive someone. (Example: Do you wanna take a ride in my new car?) "Take a ride" is not used to say that you rode in someone's car. Example: "I took a ride in his car" is wrong. (Well not necessarily, it just sounds unnatural.) Instead of this, you would say "I rode in his car" Thumb a ride = sounds weird from a younger person's perspective (people don't really hitchhike in the U.S since it's dangerous). It might be correct, however it sounds unnatural and I suggest you refrain from using it.

Technically, they all mean the same thing. However, the term "thumb a lift" is usually reserved for when you are actually thumbing a lift off a stranger at the side of a road. If I wanted to get a lift with a friend I might say "Can I hitch a ride with you?". I probably wouldn't use "take a ride" as it doesn't quite work. Instead I might say "Can I ride with you?". Hope this helps.