Luggage onboard train

My whole family (old & yound) will be travelling from Kansai Airport to Osaka (staty few days) before heading to Tokyo Shinjuku.

There will be about 7-8 big luggages. Anyone knows if we are allowed to carry the luggages up the airport express train and subway? What about JR train from Osaka to Tokyo?

Alternatively, we can take the Airport Express Bus but we still have to settle the luggage problem from Osaka to Tokyo. Anyone can advise?

There is plenty of room in both the Haruka (JR) or the Nankai Exp for plenty of luggage, though I dont take the supersized cases anymore and limit our luggage to medium sized pieces (say less than 45cm wide x 25cm deep x 60cm high). The problem with anythong bigger than that is that you cant put it in the overhead luggage shelf if the sections at the front or back of the carriage are taken, or if it doesnt have them. We travelled a few times with bigger pieces but it was a drama from time to time especially with trains and escallators and lifts, so now we travel a bit lighter (but still heavy compared to Japanese)

I usually travel abroad with a midium size backpack and buy whatever I need there.