do tubes have anything to do with volume?

I think they affect volume. If your tubes are quite old and near the end of their lives, they may sound weaker and definitely less dynamic. Output tubes in my system that are testing at 50% will have muddy bass, soft highs and not a lot of headroom.

how do I test them?

Need a tube tester. Or, find someone in your area with one and bribe/imbibe them. Pittsburgh?