PORTOLA VALLEY, Calif. — A tank museum anywhere is a strange spectacle. It documents humanity’s ingenuity and ambition, and also its desire to demolish whatever is in its path with terrifying finality.

A tank museum tucked into the tranquil hills here is stranger still. A tiny town west of Stanford University, Portola Valley is the sort of place where breezes tinged with the scent of old money and horse manure waft through picturesque woodlands, and leaf blowers that don’t even reach the noise level of a moderately crowded Manhattan singles bar are officially prohibited.

Yet Portola Valley is where you’ll find the Military Vehicle Technology Foundation, one of the nation’s most intriguing museums. On the right day, you might find Tom Sator there, too....