I second Kekkon Dekinai Otoko (also the Korean version is ok, though a bit dragged out).
Because This is my first life (kdrama) and We got married as a job (jdrama) are similar kinda.
Linus:
Tomorrow with You (he is a weirdo because of his ability to travel to the future)
Chief Kim (he is a total weirdo except that there isn't really strong romance in this one. Still, you probably won't find a guy that is more out there that the main character here)
Fated to Love You
Healer
Kill Me, Heal Me
Shopping King Louis (I did not finish this one, though)
You are All Surrounded
Chief Kim - There is strong romance.....BROMANCE! xD