The Xabungle characters, of course. The picture of a melon replaceing Jiron's head like in the show in Alpha Gaiden, is one of the funniest thing in the series.
Speaking of Alpha Gaiden, Roy Focker goes into one battle completely wasted. It's as funny as it sounds.
Also from Alpha Gaiden, when Kosuke and Usso ask Kid and Bowie how the Braiger is able to change size, they have no idea. But then their child assistants, Shin and Mei, show up and are able to explain it, though their elders still don't understand. But Kosuke and Usso do, and are even able to discuss it on a theoretical level. Cue a slight Jaw Drop from Kid and...
Bowie: Christ almighty... Kids these days are something else, huh?
On one stage of Alpha Gaiden, Loran and Milia bring out their mechs to do laundry since the Argamma's washing machines are broken. And then Kouji brings out the Mazinger Z to dry it with Breast Fire. One of the girls comments that he "would make a good bride," but he manages to scorch some of the laundry. Perhaps it's just as well that no one ever tries to make clothes for the Valsione or Angelg.
Incidentally, having Milia pilot an Armored Valkyrie will break the game since she has to transform from Fighter to Battloid in the cutscene.
The characters lampshadeing the fact that Usso and Garrod seem to attract Shotacons in Alpha Gaiden. The fact that it's Judau of all people who starts this makes it even funnier.
Around the midpoint where they crew are heading out to Zondar Epa, they ask the others to carry luggage, including The Big Guys form several series, including Fatman, who for no reason, starts doing numerous posses, leaving Marbet and Jirod speechless.