What was Big Willy Shakes going for?
For all of this to make sense, we should tell you that Caliban isn't your average islander. In fact, he's one of the most debated figures in all of Shakespeare. As the island's only native, Caliban showed Prospero how to survive on the island and Prospero took Caliban under his wing and taught him to speak. For a while, things were hunky dory. Or, as hunky dory as things can possibly be on a remote island. We even learn that Prospero treated Caliban "with human care" and let him stay at his pad.
So, what changed? Why does Prospero enslave Caliban, punish him with debilitating stomach cramps, and hurl the kinds of insults that would have most of us running to the bathroom to cry? Caliban, we learn, tried to rape Miranda in an attempt to "people" the isle with a bunch of little Calibans (1.2.4). That's pretty inexcusable, so it's clear we're supposed to be repulsed by Caliban's monstrous behavior and it's easy to see why Prospero treats him like dirt.
When thunder and lighting scare the heck out of Trinculo, he seeks cover with Caliban. The only problem is, he's not exactly sure what or who Caliban is (and either are we), so Trinculo says he's got a strange bedfellow, or person to share a bed with. Under these circumstances, Trinculo and Caliban are instant roomies, but not by choice.
In fact, it's out of misery and fear (from the thunder and lighting) that Trinculo even jumps under Caliban's cape in the first place. To the jester, strange means something foreign or unknown, which most certainly applies to Caliban.