Same here. Several years ago I had a bed with wood chips, three springs in a row there was a huge swarm of termites. I finally figured out what the problem was, scraped up all the hardwood chips, treated the area and laid shredded native Texas Red Cedar mulch and haven't seen a termite since then.
We use cedar shreds for our path from the house to the workshop, and make sure it's the no-float type. We also use it around but not in the vegetable gardens--we have a 3' wide path around the gardens to keep the bermuda grass out (HA! Lovely theory, but I still pull bermuda) and it takes about 18 months to break down to the point where we have to refresh it. I have tossed sawdust from my husband's workshop into the compost heap, but it doesn't amount to more than a couple of gallons at any one time, and that fairly infrequently. Sawdust mixed with chicken manure and composted does wonders for corn!
In this day of tobbacco based insecticides and hebicides, getting organic is a goal not a begining. As a rule the more you know about what went into the pile you are rotting, the further along you will have gone to that goal, It is true that oils slow composting, what is not true that an utter absence of any oils will speed compost along. A bag of orange peels will have no noticable effect on your pile. The full contents of a fryalator (about 9 gallons) most certainly will. So moderation in all things. I like a three bin compost. One filling. second rotting. Third being shoveled out.
