"That's different. Did Punch ever mention a Master Heliotrope?"
"No, because he couldn't talk."
"Oh my. Not many people know that."
"They probably also don't know that he hiccups after he encounters electricity."
Punch is a construct built by the young Heterodyne Boys. Along with his wife Judy, Punch as originally created is very strong , but flawed in that he shows obvious signs of being a construct, in his specific case including his huge size and being a mute, although the last is not generally known and the Punch featured in Heterodyne Boy stories speaks.   It is perhaps those flaws that might have helped disguise him and Judy in later years, for while some might see that he was a construct, they also might not accept that this 'imperfect' work could be the product of the legendary Heterodyne Boys.  Being active in the Heterodyne Boys' adventures, he has acquired some impressive fighting skills, including being able to 'flick' metal rivets at near bullet speeds with a high degree of accuracy and control. 
At some point he went into retirement and took the name Adam Clay. The "Punch" persona remained (or became) popular as a dopey comic-relief character in Heterodyne stories,  much to the annoyance of Punch and those who knew him.
When Barry returned from parts unknown with a young Agatha, he eventually put Punch and Lilith in charge of raising her, before (re-)disappearing on a mysterious personal mission. The trio settled in Beetleburg, a town run by the old family friend Tarsus Beetle, where Punch worked as a blacksmith/mechanic. Their life was reasonably peaceful for several years, despite the uneasy knowledge that Barry had been gone too long and that an old friend they now suspected of something horrible was gaining more and more power. Toward the end, Beetleburg was independent in name only.
In the Comic
Events come to a head when Baron Wuflenbach finally takes overt control of Beetleburg, on the same day that Agatha's locket is stolen. While Punch and Judy search for it, Agatha's sleep-building of her first clank ends with her being taken to Castle Wulfenbach. Fortunately the couple are skilled enough adventurers to steal an airship and track her down there, interrupting a less-than-romantic moment between their foster daughter and Gilgamesh Wulfenbach. Sadly, they are stopped on the way out by a Wulfenbach party  including Klaus and Von Pinn, who kills them both. (Although Agatha escapes in the process.) Gil takes immediate steps to patch them back together and revive them, a complex and delicate process which takes an extended period of time. Towards the end of this effort, it is revealed that Punch can now speak, (perhaps done by accident, as Gil appears startled when Punch speaks).
At this point Punch and Judy are stable enough for Gil to leave them unattended without fear of catastrophe. How soon they are truly ready for action and what they do during this period has not yet been revealed.
Time Skip (Approximately two and a half years after Bomb/Door)
Agatha is finally Mechanicsburg, where he has been working with the Jagermonsters and various refugees stranded outside the time-frozen city due to the Baron's use of the Take-Five Bomb. At first she thinks Adam is an imposter because of his aforementioned powers of speech, but is reassured by Dimo that it is really him, and informed that it is now difficult to get him to stop talking. (It's not stated, but it's highly likely that Adam is the source of Dimo's spiffy new mechanical arm.) Adam's skin color has darkened from his original appearance; it is unknown if this is an in-universe change or simply an artistic shift.with Adam/Punch in the Sneaky Heterodyne Cave near
Among other things, Adam reveals that Lilith/Judy has been caring for the children in the caves, including, to pretty much universal surprise, Adam and Lilith's biological daughter Maxinia; it appears when Gil fixes something he doesn't settle for half-measures. Agatha leaves Punch and Judy behind in the caverns when she sets out for Paris.
Outside information and speculation
When Punch and Judy kept Agatha in hiding with them as their foster child, they went by the aliases Adam and Lilith Clay. Adam was the name given to the first man in the Bible, and some myths refer to Lilith as the wife of Adam prior to Eve. Given that some creation accounts refer to humans being fashioned from clay, and that the medieval story of the Golem also refers to its being made from clay, it appears that the aliases chosen for Punch and Judy were intended as an ironic reference to their status as constructs. We have no explanation for why the name Lilith was chosen, other than that it would have been less obvious than Eve, though it does raise another interesting point for fan discussion on religion.
Their actual names, of course, are references to Punch and Judy, characters from a traditional English puppet show dating back to the 16th century in the real world. Similar shows actually exist in the Girl Genius universe, but whether the names are used in that context is unknown.