Just a side note: It’s not advised to run two different types of cabs over the same frequency range so you may want to consider that. You may get undesirable effects such as phase cancellation and could end up losing the “volume” that you think you might gain and making things sound a bit muddy in the process.

Assuming the drivers in all 4 of the cabs are rated at 4r (r = resistance in ohms), you wire them in parallel and your amp can run @ 4r on each channel then your logic is sound. It is a good idea to use an amp that has a bit of headroom compared to the driver rating. Small transients in the music (resulting in peaks in power output) can be handled fairly easily by drivers, but if you are driving an amp hard at full power and you don’t keep an eye on the signal from that redlining dj then your peaks and troughs can end up as nasty clipped waves which can do some damage to a driver. More damage than boshing more than the rated output in to a driver from an amp that has a bit of reserve.

There is plenty of reading around the internet that can be done on ohms but the ohm rating is the impedance/resistance of a driver. Wiring 2 8r drivers together in parallel would result in the amp channel seeing a 4r load. Ohm calculations can be complicated but an easy rule to remember is (provided each driver has the same ohm rating – eg 8r) then you take the impedance rating of 1 speaker and divide it by how many drivers you have wired in parallel.

Therefore:
1 x 8r driver will obviously be an 8r load to an amp
2 x 8r drivers will be a 4r load
3 x 8r drivers will be approx 2.6r load
4 x 8r drivers will be a 2r load

Which I hope also answers your last question as to why manufacturers give you the power rating at different ohm loads. Although the lower impedance allows more power to flow, it also puts the amp under greater stress. Some amps cannot handle being run at 2ohms a side (a channel) so make sure you check this. No amp should be bridged (channels combined) in to a 2ohm load. Also check at what frequency range the watts to ohm rating is given at as it will often be supplied in 1 or 2 ways. As you are running bass frequencies you will want to concentrate on the rating over over the whole “useable” frequency range eg 20hz – 20khz.

So assuming you go ahead and use all four cabs you will need to check the impedance/ohm rating of the drivers. They are most likely 8ohm, so wiring them in parallel would put a 4 ohm load on each side of your amp (2 speakers on each channel).

So with that in mind, look for an amp that can deliver over and above 700w a side @ 4ohms.

There are more electrical minded peeps on this forum that can probably explain all this in more depth and with better accuracy than I can, but I hope this helps you. I do recommend doing some reading on the internet though.. plenty out there if you use a search engine.