Here he's comparing those grand old poems (the ones he doesn't want tonight) to the sounds ("strains") of military ("martial") music. Basically, he thinks they sound like the music you'd hear during the fireworks on the Fourth of July.
Their mighty thoughts suggest Life's endless toil and endeavor; And to-night I long for rest.
The big, grand ideas in these poems make him think about how hard life is. They remind him of how much work ("toil and endeavor") we are faced with every day.
Can you see how that would bum him out after a long, hard day? Again, if you flip on the TV after a tough day, are you going to pick a really serious documentary about war? We think you're more likely to head for American Idol or that Law and Order rerun you've already seen.