Are you sure that it was oil and not fuel that was dropped ? Easy quick assumption to make, black slippery stuff under bike down on tarmac. If it was oil, where did it leak from ? How long was the bike on its side for ?
If there was any significant damage to your plastics, remove them and inspect your casings. Check oil level ( and coolant levels whilst your at it) before restarting and when you do start her up check the exposed casings whilst she’s running.
Did she fire up on all cylinders when you got her going ? White smoke could be oil or water but hopefully it will clear soon enough. Your description suggests to me that this was a minor drop and if this is the case then likely you have got away with being nice to your cousin. Let’s hope so.
Sorry about all the questions mate but the more info’ the better.
Best of luck