1. On the train, he goes to sleep.

2. On the train, he falls asleep.
3. On the train, he goes to bed.
4. In the train, he sleeps.
[Can we use all the expressions in this situation? Can we substitute 'in' for 'on'?]

#4 would not be used; "in" cannot be substituted for these expressions.

In addition, "On the train" is awkward when placed at the beginning of the sentence.

The use of "in" could be any of these -- INSIDE the train!

He ate in the dining car on the train.
She and her daughter slept in a pullman car on the train.
Their seats in the last car on the train were facing each other.