When you do something strenuously, you work really hard at it. After working strenuously on your neighbor's farm all day, you'll be exhausted and ready for a break.
The adverb strenuously is good for describing activities or actions that require hard work. You can play strenuously during your high school football team's final game, working up a sweat, or you can argue strenuously during a debate. In either case, what you're doing is seriously demanding. The Latin root is strenuus, which means "active, vigorous, or keen."