Some people get fun in trying to solve nonsensical yet imaginative unique puzzles.
So if there was a tag for “funny” or “nonsense” it would avoid irritation caused when user wrongly tags their question as something else.
What do you mean by "funny" or "nonsense"?
Tags should always (ideally) have a clear and unique meaning. But all kinds of puzzles can be "funny": it's not limited to any particular genre of puzzle. And a tag for "nonsense" would just encourage people to post complete nonsense that's not a puzzle at all and should be closed and deleted.
We already have the tag you want, and we should get rid of it!
We used to have a joke tag, which was renamed to humour at some point, although the community consensus is actually to get rid of this tag entirely, because it's a breeding ground for bad puzzles. We've been getting lots of low-quality questions with that tag, and it just hasn't worked well for the site. See the previous meta Changing 'joke' to 'humour' or burninating it for more details about that.
As for nonsense ... that sounds to me like it'd be even more of a haven for bad questions than joke! But it sounds like the existing (and hopefully soon-to-be-non-existing) humour tag is already the type of tag you're proposing here.
Once again, I think you need to be clearer about precisely what type of puzzles you're trying to describe in this proposal. Once we have a clear idea of a particular genre of puzzles, preferably with examples, we can discuss how to properly describe and characterise those puzzles, which in turn should lead us to a reasonable name for a tag.