Is any sort of automotive type motor oil or hydraulic oil suitable for any of these locations?
No Motor oils! ISO-46 will work in the headstock. Make sure your motor is turning the correct direction for the oil pump to operate properly. I would pump ISO 46 thru the apron to get all of the oiling points lubricating properly. I don't know what the larger model X is like. The standard model X, the baby to yours, the carriage/apron, saddle is a massive network of holes providing passages for oil to each of the points or oiling. There's about 30 Bijur metering units controlling oil flow. You will probably find most to be plugged up. That's why John O. mentioned using a handy Golden Rod oil can for doing manual oiling for the ways and cross slide.
The front cover on the apron can be removed to access the oil pump and to clean out all of the crud that collects in the bottom of the apron. Not a easy task to remove but not impossible either. Word of caution, that cover on your lathe probably weighs around 200 lbs. Be careful if you decide to remove it!
Somewhere here on this forum is a couple of threads that John and myself have on the 20" Standard Duty L & S we had. Actually, I bought the lathe from John and completed the rebuild on the old lathe. There is a post or two on cleaning out the oil passages on the saddle. I no longer own the lathe. IT's sitting in a lean-to collecting desert dust and rust the last time I saw it!
Ken