A "Jalopy" is usually a car from 20's-early 30's and has had a hard life. Driven to nothing and parked/junked to be forgotten. Yet, somebody somewhere decided they could be raced. They looked rough, ran rough, and the action was intense to say the least.

Jalopy Action
You might notice mostly skinny stock tires, with original frames/suspension. Some people can refer to them as "Highboys". That is just another term really, means almost the same. Basically the bodies are on the original frames (unchanneled/altered) and fenderless. Meaning running boards ripped away. Combined with the tall tires, they look like they are riding high. Some feel the term stops at 33 or 34? I could be very wroong on that little nit pick.
EDIT - I used this term on this forum for the cars Dave and Bob built. It really is used mostly in street rod culture. I just called them that because I am bad about using slang to describe a car. They are building Jalopy style cars with the skinny wheels and tires. And straight or stock appearing frame rail. I am building a Modified. I said that we could have 2 classes: "Highboy" and Modified". I suppose I should have just said "Jalopy".

The term "Modified" was used for them as they evolved and were in fact VERY modified. Some people will refer to them as Jalopy/Mods depending on who you ask.
When I say "Modified" it means later model cars that were basically shells and everything else was hand or race built.

Big tires, special built frames, race suspension, etc. These were common in the later 60's and were raced into the 80's in some parts of he country.

Modifieds could be more modern, or run older bodies. It depended on the track/rules about the class.

A banger??? Ummm, sounds like "Bomber". Meaning an old full fendered pile of junk you made race legal and raced it.
I am SURE you will get different answers. Just my quick take, and tried to make it easy.