My relatively new Omnia notes it has 8GB of space on the internal memory card. But when I try to transfer a 5 MB app (NRG Chrome Weather 3.1), it says the file is too big.
I have put on maybe four songs and three apps (Google Maps, ApiSRO, YouTube).
Make sure that you are installing to "My Storage" which is the 8 gb. If you are not installing or saving to "My Storage", then you are putting it in the device memory which is VERY limited.