I don't think you could get pornography off the internet. The government couldn't even keep obscenity off the walls of the boys bathroom at my highschool. That said, I think you could have viewing ponography online (or maybe just distributing it) be illegal. Of course, as we all know, there are kinds of pornography that can't be legally viewed or distributed, but sadly people still find ways to get around the law. The solutions are likely to be similar. Darknet websites that requires secure encryption to view, "home made" imagery being more common relative to explicitly commerical productions, images or videos encrypted to hide them in other, seemingly innocuous files.
I think there would be several cultural effects. One would be less niche porn genres. I think without the huge amount of competition and market saturation, you're likely to have more of a "take what you can get" angle. Another is going to be a much more successful market for truly awful things like child pornography. With a huge illicit market/swapmeet by people looking for more ordinary pornography, the nastier stuff can probably hide in the cracks more easily. Indeed, it may be very difficult to tell what you are getting until it is actually downloaded and viewed. Also the protections for adult film workers that currently exist, though not perfect, would be completely absent. Performers in commercial pornography are likely to be involved in other sex work, have no guarantee of protection from disease, and no one is going to be concerned about being "barely legal" when none of it is legal at all. So many performers in pornography not aimed at pedophiles are likely to still be well under legal age.
The exact penalties for porn possession and distribution on their own and relative to other related offenses like prostituion or child pornography production or distribution are likely to change these impacts. If child porn gets you locked up for years, but other pornography gets you a $50 fine, you are likely to see a lot of self policing amongst distributors and consumers to maintain a distinction. If the penalties are very close, you are likely to see much less concern about keeping the worst elements out.