If you opplever a lot of things you will gain erfaring. Experience is contextual in English. Substitute both italics with experience... Comments in brackets are from Oxford Advanced learner's dictionary.
It's an experience I could do without -> opplevelse [the things that have happened to you that influence the way you think and behave].
He has a lot of experience -> erfaring [the knowledge and skill that you have gained through doing sth for a period of time; the process of gaining this]
Oppleve and erfaring don't always fit well in the same context. As you learn and do things, acquire knowledge, they mostly come out as erfaring. But opplevelser is closer connected to amusement and personal growth and interaction with people, ie not directly into knowledge as such (unless your field of expertise is in humanities). So you can add your different erfaring to your CV, but unless you apply for the next "travel the world barefoot living off garbage and rainwater" reality show concept, opplevelser rarely has a value.
Excellent! So, if Jimi Hendrix had been Norwegian, his album would have been titled: Er du opplevde? And if I'm interviewing a job applicant, I would ask, "Har du erfaring?"
Is it correct to assume that erfaring is used only as a noun (cannot be modified into a verb, etc.)?
I think the album would be called Er du erfaren as experience here is an adjective (the experience is a trait of the subject). Har du erfaring is correct. On the other hand you can't ask Har du opplevelse, it would rather be Hva har du opplevd (what have you been experiencing). Or Har du en opplevelse å dele med oss (Do you have an experience to share with us).
The two words are a bit different in use, both can be a verb and a noun, only erfaren can be an adjective.
Verb: Å oppleve Noun: en opplevelse. The word stem is "live up", live to see what happens.
Verb: Å erfare Noun: en/ei erfaring Adj: erfaren. The word stems from German, to learn through travelling (erfahren)
Interesting questions, I learn a lot about my own language having to figure out reasonable answers :)