Would lets just say 1000 watts on 2 ohms be the same electrical strain as 1000 watts on 1 ohm?

power rating at ANY given resistance if both amps are of same efficiency will pull the SAME current.

The ohm load has NOTHING to do with how much it will pull from your electrical system.

The lower ohm load you go, typically the less efficient but that depends on the efficiency of the amps as well.

Usually, efficiency ratings.. if even given are only at 4 ohms. The lower your load, the lower the efficiency, but in your case, for different amps, you need the efficiency ratings at these specific ohm loads to answer the question precisely.

conversely speaking

the lower the impedence the more power, it will put out as well as power*current* it needs to function

I'll sort of clear this up, from an actual engineering perspective. There are, in electronics, two quantities that are specified in ohms: impedance... resistance... Both, of course, are specified in ohms.

Ohms, simply stated, is a resistance to the flow of electricity. It has nothing to do with volume, only the amount of "resistance" to the current that flows. The larger the ohm value, i.e. 16 ohms versus 8 ohms, the more resistance is offered.

There are two other values in the electricity equation... voltage - which is the potential for current flow. Just because voltage exists doesn't mean that current is flowing (i.e. similar to a battery sitting in a drawer). Current is the second... this is "real work" in electrical circuits. Current ONLY flows when a circuit is completed and voltage is present. The AMOUNT of current that flows is directly related to the amount of resistance. Less resistance = more current...

Current, voltage and resistance are all related: V=I*R... Higher voltage implies a greater capacity for more current, etc.

There is, virtually, no difference in volume between a 4 OHM, 8 OHM and 16 OHM setup IF, IF, IF, the amp is setup to handle each of those instances. Speaker volume (loudness) is a direct response to input voltage/current and a function of its sensitivity NOT impedence.

The impedance (4 OHM, 8 OHM and 16 OHM) is the resistance the amplifier (power amp) has to overcome to produce sound energy. Amps are designed to run "efficiently" at one impedance or another. Obviously, if an amp provides the same voltage, no matter what, a larger impedance MAY mean lower drive current to the speakers. As speakers are primarily current driven devices, an 8 OHM amp driving 16 OHMS MAY be "softer" but ONLY due to the fact that the current flowing in the speaker/amp circuit is halved.

Conversely, an 8 OHM amp driving a 4 OHM load MAY be louder but that's due to the fact that the amp/speaker circuit has twice the current (the ability to do real work) flowing. This impedance mis-match MAY destroy your power amp. MORE CURRENT FLOWING = MORE POWER REQUIRED. LOWER IMPEDANCE = GREATER POWER REQUIREMENTS. Amps spec'd at 8 ohms, running 4 OHM loads have to dissipate more power in the amp... if it's not made to do that it can destroy the amp...

SUMMARY

Impedance/resistance, is specified in ohms. It refers to how much resistance is offered to the flow of electricity in a circuit. The larger the ohm value, the more resistance is offered. The lower the less. Lower impedances = more current flow and more power required. Higher impedances = less current flow and less power required. Loudness levels are dependant upon speaker sensitivity, not current draw in an amp.

The real question is why do you want to know and what amp are you talking about. There is no generic answer to your question as it could be either way depending on the design of the amplifier.