while there are many factors, it may be best to just go off the voltage reading only. here is why:
why do you want to measure power? Normally to benchtest an amplifier. This generally is done to compare amplifiers, in which case standard conditions (test load, distortion limits, ect) are needed. Another use is to determine how much power your woofer is getting. But a simple voltage reading is sufficient to determine more power or less power.
So at this point you can upgrade, either to a clamp meter, or a crude OScope. the OScope can give you information on distortion, which can make the more/less power WITHOUT DISTORTION measurment more accurate, though it cannot garuntee that the amp will not clip if the battery voltage falls.
The clamp measures current. But, because the speaker can convert electrical energy to mechanical energy (and back), impedance can change with freqeuncy, and in sealed boxes this can be very significant (eg, by a factor of 10). because the woofer tends to be very efficient at such frequencies this reduction in power isn't noticable. So this means that you can end up reading something small, like 50W. (at 40 ohm) instead of 500W (at 4 Ohm). Also, you cannot measure distortion as effectively. But, you can measure impedance rise from this.
Also, you don't know if the peaks of the voltage align with the peaks of current. such a condition occurs when energy is put into moving the cone (or compressing air) only to be reclaimed at a later time. This makes it very common. still this "bouncing" of energy is "conservative". it isn't power as, over a long period of time no work is actually being done. but it does cause the DMM and Clamp to read high voltages and high currents. A 2 channel OScope with a current probe can allow you to see both voltage and current and how well they line up. More advanced versions will have a multiply function that can plot power (and find average power) over time. They may also have spectral analysis (FFT) allowing a measurement of distortion/noise.
but at the same time, is this much information actually useful? for learning, yes. for developing DIY equipment, yes. for researching speakers? yes. for benchmarking amps, not yet (still need a standard test load). for tuning boxes, yes