How old is the child? How is the child managing in the classroom? Does he have an aide? Is he verbal?
Many autistic children benefit from a daily planner of the days events. It can be extremely useful to set up a visual picture schedule e.g. 10am OT with a photo of you, 12pm lunch with a picture of food, 3.30 home time with a picture waving goodbye. His aide could take him through this schedule at the beginning of each day. He may also benefit from active seating such as a move n sit if he is craving movement. Perhaps consider other organization strategies also such as colour coding books (green= spelling). Also social stories may be useful.
In terms of vestibular & proprioceptive activities it is definitely harder without a sensory room of some description, although I guess a reality of what many parents face at home.
Some activities I have had success with have included:
-Peanut/ gymball- sit on this and bounce up and down, or roll over it on tummy and press hands into floor (check the sports cupboard, these are also cheapish to buy). I also have the kids lie down and roll a fitball/ gymball up and down their backs (great for calming).
-Crash mat- squashing/ sandwiching kids in a crash mat/ blankets (great for calming). (You can make a cheap one by sewing together a duvet cover stuffed with rubber offcuts).
- Encouraging 'heavy work' in the classroom such as wiping down tables, helping to move furniture, pushing chairs in, helping roll the TV into the room etc.
-Swinging (I know you don't have one but what about in the playground?)
-Jumping on a mini trampoline (check the sports cupboard)
- Animal walks (crab walks, bear walks)
In addition, I find bubbles (blowing, chasing, catching) a pretty big hit generally as well as musical instruments (playing drum, keyboard). Quite motivating for kids.
If he is disruptive in the classroom, it may be that he needs a sensory diet that can be completed at various intervals during the day.
It sounds like it is very difficult to engage him. Sometimes I just have several activities set up in my room (e.g. put out a fitball, crash mat, some drums and a puzzle) and then just follow the child's lead as to activities.
Good luck.