Male lead is a weird, but sweet/nice guy

That Fool

Hogo's Love

Hi my Sweetheart

We married as a job

Healer - the male lead doesn't "live like other people" to quote the drama.

Live Up to Your Name - time travel + goof ball = a good amount of weirdness.

It's Okay, That's Love - the fact that they're all dealing with their own weirdness is pretty much the premise.

Gu Family Book - half gumiho.

Pinnocchio - weird circumstances make the male lead weird. He gets a nice makeover later.

Moon Lovers: Scarlet Heart Ryeo - male lead is an outcast in his family because of his mother, circumstances of his upbringing, and the scar on his face. He's a bit dark and on edge as a result.

Kill Me, Heal Me - multiple personality disorder.

Goblin - title says it all. 

You Who Came from the Stars - 400 year old alien is still learning how to interact with people.

Strong Woman Do Bong Soon - male lead and female lead are both weird in their own ways.

Introverted Boss - probably more what you were looking for. The boss has a certain level of social phobia / is extremely shy.

I never finished My Unfortunate Boyfriend but he was an odd one, wasn't he? :)  No Min Woo is also in the web drama Eating Existence, and his character there reminded me a bit of My Unfortunate Boyfriend, so that might be worth a shot.

It's still airing so I guess the jury's out on who ends up with whom, but you might try The Package. The male lead is a little bit naive and bumbling but a good guy.

I'd also second Hogu's Love, although Hogu is definitely more on the sweet side rather than weird, but he does have his moments of weirdness too.

We married as a job

Densha otoko

That fool

Ouran high school host club

The first one that comes to my mind is

Because this is my 1st life

(He is sooo weird loool.. He has hilarious ways of living.. And he is nice and sweet too)

Also cheese in the trap- he is very weird to the point that we cant understand what is going on in his mind. Lool. But after some time, he becomes suddenly nice to the female lead.