Etymology
From Dutch nodigen or its dated variant noden (both “to invite”), respectively from Middle Dutch nôdigen, nôden (both originally “to force, compel”); related with Afrikaans nood, English need. The shorter form yields Afrikaans nooi through regular d-loss (cf. dooie < Dutch dode). If it is from nodigen, the -g- must have been elided additionally. This does not normally happen in unstressed -ig-, but would still be likely here because of the postvocalic environment, i.e. nodigen > *nooige > nooi(e). See: Dutch '
nodigen'.