I was looking for them as well but I didn't find them

For now I found the songs in episode 2 *wipes sweat*.  I am going to look for the rest next.

전영록 - 종이학

오동동 타령

전영록 - 내사랑 울보 

최호섭 - 세월이 가면

바람, 바람, 바람 -- 김범룡

OMI - Drop In The Ocean 

Dear - Mad Soul Child

이정현 - '그 누구보다 더'

Thank you for the link. I'll check it out. Oh lucky me I've only watched up to episode five! 

Here are episodes 3 and 4 songs

EP3

웃는 여잔 다 이뻐- 김성호

이정현-한 여름의 크리스마스

Cho Yong-Pil - Short Hair

강수지 - 보라빛 향기

Des´ree - Kissing You

김정민 - 마지막 약속

임백천 - 마음에 쓰는 편지

EP4

빛과 소금 - 샴푸의 요정

소방차 - 어젯밤 이야기

love potion number 9

구창모 - 희나리

가리워진길 - 유재하 

Omg thanks so much! Yeah, I've been using shazam and soundhound for the instrumentals, but also for the Korean songs because I don't know how to write the Korean words I hear (Korean spelling eludes me...). I also tried to use Naver Music, but it didn't really offer me up any results. 

I've found that the creators were really funny and made a ton of references to other pop culture shows and movies. Speaking of which, there's a karaoke song when you get to episode 5 that I couldn't find. It's the second one they're singing, if you can transcribe the korean and look those lyrics up!

You're the best!

 Peephole:

I couldn't transcribe it. I copied the title from the karaoke screen

It is 박남정 - 널 그리며 

Thank you very much! I want to play this song on the ukulele. Found uke chords on this site, a good resource for lovers of this musical instrument. Here you can find chords for many songs, learn to play them, and develop your musical skills