i wouldn't label it as jargon --> jargon refers to well defined terms that people that are in the bizz all comprehend and use with the same meaning. like 'normalized database', 'recordset', 'persistent connection', 'bug' etc. And you realy need to know your jargon to be able to efficiently communicate with other people in the bizz.
here this guy is just using (at best) some company-specific terms.
if somemone is using such vague/ambigues terms, i just ask them what they actually want to say, in a non-confrontational way of course. people that ask clarification are, in my opinion, at least interested and in most cases will be confident enough in their own ability to have a serious talk about the subject (after possebly picking up some new stuff).
i often will also rephrase their comments/questions/etc to make sure i'm on the same page (and to let them know i'm following what hey are saying).
of course, you can also mix in a few vague terms yourself. Like "We use a human interface to generate most of our code."
i think that the worst think you can do is pretending you know what they are talking about. I would never hire anyone that doesn't ask clarification --> in most cases, such employees start on tasks without fully understanding what is desired.
you should definitey read up (and experiment) on OO. Googling for 'PHP OO tutorial' should bring up enough for you to start with, but the main thing is that you read a lott of code (not from 2-page tutorials, but pick a class from www.phpclasses.org
or so and read through the code + look up everything you don't understand in the manual) and write some classes yourself.
as for the transition from one skillset to another --> what sort of mainframe stuff did you do? is there a lott you can reuse?