I grew up in Philadelphia and the only one of these I know of is olive loaf. Can’t say I’ve ever experienced it, but I know it’s available because a few years ago a pregnant co-worker craved a bagel sandwich with olive loaf for a few weeks straight.
Parents, uncles and cousins did enjoy a good liverwurst on rye . . . with onions and spicy mustard. Always a Guinness to wash it down. But it didn’t come in a tube; it was sliced (thick) at the deli.
As a kid, I was a genoa salami or lebanon bologna kid. Rye bread was optimal, but a kaiser roll would do in a pinch. Yellow mustard. Crush the Herrs or Wise potato chips onto it at the last minute.
Parents were lunchmeat snobs . . . it had to be fresh sliced at the deli, never packaged 
I continue that tradition and admit that, as an adult, I still indulge in those sandwiches a few times a year.
