A multimeter might help. But probably not unless it actually measures AC power directly. Power is current times voltage, but with AC power, you need to know the phase of the current and voltage. You could find an upper bound this way though.
I run tiny tiny rss, which needs a php, webserver, and SQL backend, on my Raspberry Pi. It runs fine. Of course, I'm sure if it needed to serve more than one user at a time it'd do poorly.
Any chance you could sell that server for like $30? Or its parts? The CPU and motherboard probably won't fetch anything these days (though who knows, maybe someone wants an old low end server for some purpose) but the hard drives might fetch something.
You need to find out the marginal rate of electricity. Pull up your electric bill and see how much they're charging you per kWh. Most of the time they'll have several lines with a @ $0.X/kWh notation. Add up all those rates, and multiply it by 0.1 kW * 24 h/day * 365 days/yr to get your yearly cost.*
*This is going to be slightly less than your true rate, because oftentimes there are also taxes involved. But now we're talking about a percent of some cents per kWh.