Yes, you can run strings on a Windows exe from Linux or a Mac. I just tried this and it gives everything from "!This program cannot be run in DOS mode." to DLL names to Windows function names. However, Windows text strings that get displayed are 16-bit so you need the "-e l" flag to see them; this flag works on Linux but not Mac.

TL;DR: running strings on an exe is trickier than I expected, but works.