Reply by rob_port

With MDF and particle board waste I wouldn’t use it for composting or animal bedding. If you can separate out your waste into wood and engineered wood, I would suggest using the wood sawdust as WDHLT15 suggests.
I mix mine with urine and leave it as a mulch 1-3’ from plants I want to feed, so that they don’t get an ammonia shock.
For the engineered wood waste, I’d probably save it and use it as an aggregate with cement where I need stiffness but not massive loadbearing.