The pressure-pack cans of carburetter cleaner from the local auto DIY places are also good for de-oiling cracks and splits before repairing. Just remember to use this stuff outside, away from naked flames. And leave the timber aside for a while, in the traditional warm, dry place (on top of the water heater is good) to completely eliminate traces of the solvent. Wedging the splits open with toothpicks or (used) matches helps things along.
As for the glue: Choose your poison, but Peter's advice on the aviation-rated stuff is very sound.
Once you have worked the glue into the required locations, you obviously need to clamp things firmly.
Instead of Heath-Robinson arrangements of carpenter's clamps, I use long strips of rubber from old bicycle inner tubes, Car-grade strips are good for the bigger jobs like household furniture, etc.
If you tension the rubber strip as you wind it around the work-piece, it is amazing how much compression is achievable. To avoid new damage or distortion, don't forget to add suitable dowels and blocks of scrap to barrel channels and magazine wells before starting compression.
There WILL be some adhesion of extruded glue binding the rubber strips to the timber, so some detailed "cleaning" of the joint will be required before final finishing and re-oiling. I usually use a seriously sharp 1" wide wood chisel to gently shave away any excess glue and attached bits of rubber. A small spokeshave may do as well, but, with a chisel, you can see exactly what is being cut at all times. Clamp the wooden bit up firmly in soft padded jaws in a vise and use BOTH hands on the chisel; less crying and bloodletting that way.