(Buffalonian bison) (Buffalonian bison intimidate)] intimidate (Buffalonian bison).

[(Albany cattle) (Utica bison bully)] intimidate (Syracuse oxen)

[The] Albany cattle (that Utica bison bully) intimidate Syracuse oxen.

In this sentence, "cattle" are the subject, and "oxen" are the object. The verb is "intimidate". Everything else is some form of adjective modifying "cattle" or "oxen"

We can go further:

[The] Albany Cattle (that Utica Bison bully) intimidate [the] Syracuse oxen (that Poughkeepsie yak deceive).

Cattle are still the subject; Oxen are still the object.

The cattle (which are bullied by the bison) intimidate the oxen (which are deceived by the yak)

Moving on:

[The] Albany cattle (that Utica bison [that Buffalo buffalo buffalo] bully) intimidate [the] Syracuse oxen [that Poughkeepsie yak deceive].

The cattle are still intimidating the oxen. Which cattle? The cattle that are bullied by bison. Which bison? The bison that are buffaloed by buffalo.

Which oxen? The oxen that are deceived by the yak.

The buffalo buffalo the bison; the bison bully the cattle; the cattle intimidate the oxen. Which oxen? The oxen which are deceived by the yak.

Buffalonian buffalo [who] Buffalonian buffalo bully, bully Buffalonian buffalo

for me splitting the groups made the sentence make sense: NJ people NY people bully, bully NY people

It helps somewhat to replace “Buffalonian buffalo” with “people”:

People (that other) people intimidate, intimidate (other) people.

Well, that worked. Still, it seems off. If someone were actually writing or saying that, they would most likely use "said" or "wrote" for a at least a couple of those hads.

"And, per se, and"