Wow! I can't believe they didn't take the blocks off the ends of the speaker wires when they took their distribution system with them. Those blocks can be tough to come by, and likely won't work with whatever you purchased.
The ceiling speakers are standard speakers. 99% likely to be 8ohm speakers.
The speaker wiring will be standard 12 to 16 gauge speaker wire. The red/black wires should be connected to the + and - terminals of one speaker in a room, while the white and green will be connected to the other speaker's + and - terminals. Each one of those cables with 4 wires in it goes to a room in your home. Hopefully, the white jacket is labeled with where it goes to.
Do you have volume controls in the rooms?
Do you have keypads or something else in the rooms?
If you do have keypads in the rooms, please take a photo and post it. Maybe several photos. You may want to pull one out and get a make/model #.
If you have volume controls in the rooms, then you will want to just let us know. Volume controls means that the speaker wire you currently have runs through those volume controls.
If you have no keypads, and no volume controls, then we can talk about your options. The links in the previous post are worth a look at.