Your intended project sounds interesting. I like the idea of retasking older audio gear into modern multichannel sets. One good reason to use older equipment is that the specs, interfaces and interoperability are standardized so you can tell if/how a given amp and speaker will work together. I do it myself.
It looks to me like you have only part of an HTIB (Home Theater In a Box) system that uses a proprietary 8-pin connector and system cord that would come from the base unit/DVD/receiver (the 'brains', which you don't have). It doesn't appear to be designed for compatibility with other units, say, something that would bring in the 5.1 channel audio via either a digital (SPDIF) cable or via 5 separate RCA audio cables.
This subwoofer is self-powered and also provides amplification to up to 5 other speakers, two of which you have.
Their connection to the sub would be via standard speaker cables, likely the Red and White FRONT spring clips. The output terminals are rated up to 16 ohms so attaching a foreign speaker should not be a problem other than its having unpredictable frequency response.
Besides basic connection and signal processing, the missing DVD/Receiver would also decode and direct the 5.1 channels to the Sub and handle level matching of the channels. Without the 'brains' of the system you'll have to get creative to use the individual parts. The 8-pin input connection will be a big problem unless you're adept at getting inside the unit to figure out where things go before they come out at the speaker terminals. Then you'd have to do some rewiring.
UNDERSTAND THIS: Those connectors are OUTPUTS to speakers, not inputs from an Amplifier. If you hook that up wrong you better have a fire extinguisher handy. Kidding. But it could be bad.
The Front speakers are 3 ohm impedance, clearly designed to be used with the amps inside the Sub so I would be careful in trying to drive them with amps that aren't good at handling low impedances. Give it a try AFTER checking the low impedance tolerance of your amplifiers, but easy on the volume.
I would not expect all of this to be a worthwhile effort unless you just like the challenge. Even if you succeed in making a satisfactory electrical connection with your multichannel source as input there is no way to know if it will sound okay. With all-in-one systems the manufacturer may have matched the speakers up with special amplifiers that are designed for 3-ohm speakers and to shape the sound through active internal equalization in such a way as to produce flat response from non-flat-responding speakers - like Bose does, for example, but at least they tell you that's the case.
The stated spec is 200 watts (RMS) per channel at 3 ohms at 100Hz with 10% Total Harmonic Distortion, a very unusable spec. True and honest watts/channel specs look like, "XX CONTINUOUS watts per channel, all channels driven into 8 ohms (20 Hz - 20 kHz, +0.5 dB, -3 dB less than 0.5 percent THD)".
At only 27 lbs with a Power Consumption of only 160 Watts I'd say the Amps/Sub component of the package is a lightweight, literally and figuratively. Apples and oranges when compared to grown-up audio components. It might get loud but not cleanly. But that's just my opinion.
Here's the Owner's Manual for the entire kit...
There's some discussion of the features, etc, here...