'Get in/into' and 'get on' can all be used to mean enter a vehicle or mode of transportation. The difference is we generally use 'get in/into' for vehicles such as cars and taxis, small boats etc. Vehicles that it is necessary to enter by moving down and in. 'Get on/onto' is used for vehicles or modes of transportation such as buses, trains, planes, ships etc,. Vehicles/ modes of transport that it is necessary to enter by moving up and in.
Both 'get out of' and 'get off' are used to mean exit from a vehicle or mode of transport. 'Get out of' is the opposite of ''get in so the movement for exiting is out and up. 'Get off' is the opposite of 'get on' so the movement for exiting is 'out and down'.
Get on and Get into, Get off and Get out of also have many other meanings where the pairs are not synonymous.