What type of material are those 'staged' table made of that are used during wrestling matches?

Most Tables since the late 1990s have been Stock Department store Particle Board Tables.

occasionally they have 'gimmicked' them in either direction, to make them more stable, or more fragile... but at their core they are all simple 'banquet tables' made of compressed sawdust, aluminum frame, and metal legs, with a wood-grain 'sticker' across the Top

on occasion they will remove the Frame, as the loose metal is one of the biggest hazards

Shredded compressed wood. Like grabbing a handful of shredded cheese and you squeeze hard with your hands to make a cheese ball.

Like John Desani said, some are prop tables, some are not. RVD almost lost an eye going through a normal table during his ECW years, that's why WWE uses prop tables, to better manipulate where the broken pieces go to.

I think the tables are made of some type of cheap wood. I was once told that they cut the tables in half and glue them back together. I'm not sure if it is really true because sometimes the tables refuse to break.

Depending on what the table of made of they will also "gimmick" the table at times. In other words, they will make a saw cut that is part of the way through the supports and the table top. Then when a wrestler lands on it the table breaks and collapses.

They're regular folding tables you can buy at WalMart

Compressed sawmill.

Strong enough to hold a wrestler lying on the table, weak enough to get slammed through it.