Wood – Will walnut work for an office table

The 45 miter will be your best bet into the corner. Aside from that, please do consider where you want your joints carefully. I would keep them separated as much as possible, yet not in an area where I am going to work at, unless, you are going to sand and finish the top in place and you are certain that you can get the joint relatively flat and smooth. In my opinion, where you have drawn them on your sketch is too much in one place and will draw your eye to that place, not in a good way. Unless you are like me and there will be crap all over the place anyway.... Set the small piece on the other end, that is if it is not going to be a problem there for some other reason.

To join them, I would use 2 products.

Biscuits, and a type of countertop fastener

which I do not know the name of, but you get the picture :).

Glue is always good too.

I made a sketch when I first seen your post , I thought this was an idea too, but it may make the corner piece way too big....

It would be helpful if you could add a picture of your desk to your question. The commenters are correct. A work table with 2x4 legs is probably not fancy, and doesn't need a fancy job to raise it. If it were my project, I would either replace the legs with longer ones, or add a 5-1/2" stub under the leg while scabbing a full length 2x4 leg to the inside of the original leg. Use 2-1/2 inch screws and horizontally screw the new leg into both the old leg and the stub. You can optionally toe screw from the original leg into the stub - just like a pocket hole, but less of a process.