The wall plate you showed has what are called 5-way binding posts for speaker cable. They can accept bare wire, spade lugs, pins, or banana plugs. If you use bare wire or pins, loosen the threaded ring (as shown below),insert the wire (first twist the strands together) or pin into the hole on the side of the post, and tighten the ring.
It's much easier to use
banana plugs such as these. Simply insert the banana into the opening on the end of the post. Those threaded rings don't serve a purpose with banana plugs, just tighten them before you insert the banana plug.
You can buy standard zip cord wire (16, 14, or 12 gauge) in any hardware store and attach the banana plugs yourself. The plugs come with easy & clear directions. It will cost you more to buy speaker wires that already have terminals attached. It will be a tiny bit more convenient, but they will not function any better.
The simple 2 channel Sony receiver you bought
can only may or may not operate two speakers at a time. (Correction, see next post below.)
You cannot easily attach it to a pair of indoor speakers AND that pair of outdoor speakers you have. You would have to disconnect one pair of speakers behind the receiver and connect the other pair, going back & forth each time.
An alternative is returning that 2 channel receiver, and instead get an audio video receiver (AVR) capable of hooking up a Zone 2 system. Your wall plate, labled Z2L & Z2R, suggests the previous owner of your house did that.