At the airport, you can get a luggage trolley before getting your bags from the luggage claim area. There is only a very short walk through the terminal, before you can take the lift with the trolley down to the train platform.
Depending on which train you take from the airport to the main railway station, there are luggage racks with more or less space immediately at the entrance to the train carriages, but I would not rely on finding room there. You may have to lift, or get help to lift, your bags onto overhead racks throughout the car.
At the main station, the tracks are at a level below the main station hall. The train from the airport will usually not arrive at the same platform, from which the trains to Bergen departs. There are no trolleys or lifts/elevators at the central station and you must expect to carry your luggage. There are inclined conveyor belts between the platforms and the main station hall.
At the train to Bergen, there are some luggage racks at the entraces, but you must expect limited room. Just as on the train from the airport, you may have to lift or get help to lift your bags onto the overhead racks along the train car.