Hello and thank you for coming to Just Answer. We appreciate the opportunity to help you with your questions. If you are just a homeowner and not a professional garage, then legally you don't have to clean up a used oil spill to any environmental standards. If you clean up any loose oil that hasn't been absorbed by the wood, then you will have removed most of the hazard for people or pets. There really isn't any way to remove the oil from the wood that has already been absorbed. You are correct in deciding that replacing the plywood is the only way to remove the oil from the floor.
If you put kitty litter on the spill, let it soak overnight, and then collect the kitty litter for disposal; this will remove any oil that hasn't soaked into the wood yet. Once you have removed any free oil with the kitty litter, there really isn't any hazard to people or pets unless they chew on the wood. The wood will be slightly more flammable, which is important where you live, but since it's in your shed, the increased flammability won't be a problem if you have a grass fire, since the shed would have to start burning first. You would want to be careful of open flames and heat around the area where the spill was. Replacing the plywood is an excellent idea and it will remove the risk of fire or contact with the contaminated wood by people. I don't think you need to worry about replacing the beam, even if the used oil reached it; because any hazard from the oil soaked into the wood requires either contact with the wood or the wood catching fire and, from your description, the wood beam is covered so that it won't be accessible once the plywood is replaced.
Most cities and towns have waste separation areas where they collect types of waste for disposal. They will be grateful if you tell them that the plywood, the kitty litter (if you need to use it), and any other materials you dispose of have been contaminated with used motor oil so that they can dispose of it properly.
It sounds like you are doing all of the right things to clean up this spill and there isn't much more I can recommend beyond what you are doing. Please let me know if you have any specific questions about your cleanup or if you would like me to explain anything further. I will be happy to provide you with any further information you would like.