Resort, refer, apply, go, turn are comparable when they mean to betake oneself or to have recourse when in need of help or relief.
Resort often implies that one has encountered difficulties or has tried ineffectually to surmount them; when it carries the latter implication, it often also connotes an approach to desperation.
Refer usually suggests a need of authentic information and recourse to someone or something that will supply such information.
Apply suggests having direct recourse (as in person or by letter) to one having the power to grant a request or petition.
Go and turn are more general but often more picturesque or dramatic terms than the words previously considered, for they directly suggest action or movement.