One-punchman is fun and that is all that matters. And no, you can't take it seriously. It pretty much the same over the top parody of tokusatsu superheroes as Kinnikuman. Only with Murata's more detailed, realism oriented art to suit the deadpan humor.
Originally Onepunch-man was a webcomic done by the writer, One, alone. It has run independently for some years, I believe. At some point One got noticed by Murata Yuusuke. They collaborated on two one shots that were published this year in Young Jump.
Onepunch-man is their latest project with Murata doing the art now. It's published in the online spinoff of Young Jump,
Tonari no Young Jump. 17 chapters are out already.