Wow, that's a complicated fix, even if you're doing a quick repair just to sell it. I'm not a luthier, but I apprenticed for two years as a young man and learned a few tricks that have been helpful in maintaining my own instruments.
Part of the problem is that the wood is not just decorative; it has to maintain a certain strength or normal knob usage will quickly destroy your repair and perhaps damage the wood to the point that another repair would be even more difficult and costly.
I would suggest using animal hide glue, it flows well, it cleans up easily, it is very strong, and you can even color it to help hide the repair. Some may suggest using an epoxy but that will be too stiff as the guitar?s top is under a bit of pressure when in use and it's not forgiving when any movement is involved and let's face it, vibrations are what create a guitar's music. Hide glues are what your guitar is built with, not epoxy, and a hide glue allows you to completely redo your repair by applying heat to the mated pieces and work them apart to remove the glue and start over, you can't do that with epoxy. I think you?ll be happier with the animal hide glue, it will create a bond stronger than the original wood yet gives you the option of reconstruction if needed. If you can, you might want to try the kind of hide glue that you have to heat before using (but in reality you might not want to deal with using it; it's a great bonding agent but requires more prep work and something to heat it with). The wood appears to be mahogany so oil should not be a problem but I would take some rubbing alcohol and wipe off the mating surfaces of the break before applying glue. Make sure the mating surfaces are clean and dry before gluing.
You should utilize a backing piece (or pieces) that will be glued to the inside of the good wood and the inside of the broken wooden pieces. You might use one small, thin layer, or several thin layers laminated together to mirror the curve of the wood, or some small strips that would resemble stitches on a scar and are sanded to also mirror the natural curve of the top of the guitar).
Start by loosening the strings the night before your planned repair to take tension off the top of the guitar (you?ll need to be careful when you tune it up again making sure the tension doesn?t wreak havoc with your repair. If your goal is a quickie fix, I would then glue the broken pieces together being careful to make sure the separated surfaces are clean and glue covers all the mating edges. You should create some thin strips to use as bracing glued to the inside of the breaks.
I would start with the two pieces that surround the pot?s hole; then let it set up as per instructions on the glue you?re using. Then glue the third piece to the unit and let set up. Hopefully they?ll maintain the arc they originally had. It would be a good idea to create some bracing strips and glue them to the inside of the repaired piece along the seams when they split but don?t brace the outside edges of the piece where they meet the guitar?s top, you?ll put another brace on the guitar top. Glue and clamp the pieces and let set up.
Now comes the fun part. Make sure your repair fits in the space it once occupied and all edges match, you?ll need to make any corrections and bracing at this point. I think a thin strip of wood the length of the split (well glued) should suffice. The bracing you use should be dependent on the weight of the knob and the pressure it exerts on the wood in normal usage. Glue the brace to the inside of the guitar (not the repaired piece yet-in other words, if you have a 6? long split and a 1? wide strip to cover that length, glue ?? of the strip on the inside of the guitar leaving the other ?? ready to accept the repaired piece), clamp, let it set up. Install the pot in the repaired piece to avoid any stress after you?ve glued it to the guitar (if you?re going to change the knob do it before installing the pot into the repaired piece). Then take your repaired piece and glue it to the guitar and the bracing you constructed, clamp, let set up.
I can?t guarantee that this repair will be strong enough to last long, it?s certainly not intended to be a true permanent fix, but it should endure long enough to sell it and then some depending on how the guitar is handled. For a longer term fix you'll need to fabricate a brace that is A) not easily seen when looking at the guitar normally, B) strong enough to support the pot (my guess is that it?s the volume pot for the bridge pickup), and C) not too big so as to create unnatural pressure on the top and bottom of the inside of the guitar, in other words it must be fitted correctly.
You're probably familiar with the Steward-MacDonald web site, they offer articles about a lot of different repairs that they have done to guitars (good instructions as well as supplies - and yes, they try to sell you their products but everything you need should be found at a Home Depot).
Here's a link to Stew Mac
http://www.stewmac.com/?gclid=CKzMzrjj6LECFQ-R7QodTE4AXA
Or if you want to avoid all this, sell it so some handy guitarist and let him/her fix it for themselves.