With neither/nor and either/or constructions, the verb agrees with the closer subject.
Because girlfriend is singular, you'd write, "Neither my friends nor my girlfriend has called me."
If you switched the order of the subjects, the correct sentence would be, "Neither my girlfriend nor my friends have called me."
Aline is correct.
Using the singular form of the verb does sound odd because there are two subjects, but when we use the word neither, it doesn't matter whether the compound subjects appear to be plural or not. The rule is, as Aline stated, the form of the verb must agree with the subject that is closer to the verb.
I want to go in with a long grammar explanation but HAS just "sounds correct" in my head..