How do I change the properties of several objects at once?

You probably need the change ("wrench") tool available from the GUI. But it might also worth considering using some Eagle commands for that purpose.

Assuming for example you want to change the thickness of your wires to 30 mil, first you have to select those tracks as usual, then you might issue the following commands:

change width 30 mil
(> 0 0)

The (> 0 0) part simulate the right-click required to apply changes.

If you need to change the thickness of all the wires, this might be scripted even further:

display none top
group all
change width 30 mil
(> 0 0)
display last

Yes, the "group" paradigm is what you're looking for most of the time. Yes, it is as clunky as you think it is. There's no premade magic command. You can shift+drag (pretty sure it's shift, maybe control, been a while) selection boxes to add more objects to an existing group selection.

One thing you can try is to turn off all layers except the one you want to modify and then box select everything and use the group tool that way. Other than that, you may want to look into Eagle's ULP/scripting functionality to make yourself a command.