They are related but are not the same:
Acudir entails its hypernym ir, but moreover you go because you know in advance what happens or is gonna happen there: maybe it's an appointment, a public/private service, party or public event.
Asistir prototypical meaning is closer to witness or attend. The verb is frequently used for attending public events or witnessing relevant phenomena:
Asistí a la inauguración / I attended the opening.
Asistimos a un profundo cambio / We are witnessing a major shift.
So, asistir doesn't entail ir: this difference between asistir and acudir it's pretty clear when using progressive aspect:
Estamos acudiendo a la ceremonia / We're going to the ceremony.
Estamos asistiendo a la ceremonia / We are attending the ceremony (but never translated as We're going to the ceremony because you're already there).
Asistir is sometimes close to acudir but, in my opinion, in a passive way. For instance, I would use acudir here but I wouldn't use asistir because you have an active role:
Acudí a la comisaría para denunciar / I went to the police station to report
*Asistí a la comisaría para denunciar / I went to the police station to report
- acudir entails ir, and sometimes entails asistir (passive role, witnessing). You acudes a an event or to undertake action, and not just to a place.
- asistir is closer to witness. It entails neither acudir nor ir in every use: you can asistir to some event you did know or didn't know of in advance happening at your current location without involving any movement.
- With regard to the examples you provided I think you can use any of the aforementioned verbs (acudir, asistir, ir): 1) particularly there is no more information for the event acudieron en masa, so ¿asistir or acudir? 2) it depends on whether you want to be precise or not: in very formal contexts I would avoid ir because it's a very generic verb; acudir and asistir are not extremely formal, and you can hear them sometimes depending on the speaker.
SOURCE: native speaker of central Spain variety, reflecting on my own language use.