Yeah, each BON makes it completely confusing. Of the states listed, I only have a Cali license, and I got this before the new restrictions.
Since you have your license originally from AL, you are eligible for licensure by endorsement from all the other states. This means that you do not have to retake the NCLEX, the states just have to verify that your license in AL is in good standing. Unfortunately, you cannot do this online since AL is not a member of the NURSYS system. You will have to apply using the mail in form for each state. NJ and NY I believe are compact states, which means if you get a license in one, you can work in the other one with the same license, no problem. The only loophole here is that your original state of licensure must be a compact state as well (not sure if AL is).
You will have to mail your application form, fees, transcripts from your school, and a release from the BON in AL to the states you are requesting. They will process this, and then give you either a temp license (which is effective immediately for up to 90days), or a permanent license. CA now reviews transcripts, and if you do not have the educational requirements, they might not give you a perm license until you have all the courses necessary. You also have to do the LiveScan fingerprinting, which crosschecks your prints against the criminal database.
Usually, your recruiter can walk you through the details. Hope this clarifies it a little bit more.