What is the significance of this quote to the play as a whole? "Misery acquaints a man with strange bedfellows."

This is a witty line more than anything alse, as it is literal. Trinculo is speaking about the fact that in order to avoid the horrific storm, he's forced to share his sleep or area with Caliban, who is for lack of any other description terrified.

The strangeness Trinculo speaks of can be seen in a few different ways, as their meaning isn't defined. It can mean a "strange bedfellow," which they were, or it can also mean "foreign," "unknown," or "odd."