When a singular and a plural subject are connected by either/or, neither/nor, or or, put the plural subject last and use a plural verb:
(1) [Neither Annika nor the others] are available.
(2) [Either Annika or the others] are available.
(3) [Annika or the others] are available.
(4) [The serving bowl or the plates] go in that cupboard.
In a case like this, that is, when we have two conjoined noun phrases functioning as the subject, we want the verb to agree with the closest noun phrase head. Since it feels awkward to have singular agreement when one of the noun phrases that make up the subject is plural, it is a good idea to put the plural noun phrase closest to the verb and have plural agreement.