What does 온가지 mean?

ANSWER: 온가지 is the original form of 온갖, which means "all (온) kinds of (가지)."

One interesting Korean spelling rule is that if a word ends in a vowel, sometimes that vowel can be dropped, and the remaining consonant in front of it can be used as the final consonant of the syllable just before it. So, in the case of 온가지, the vowel "ㅣ" in 지 is dropped, leaving just ㅈ, which is then added to the syllable 가 just before it, forming 갖. That means that 온가지 becomes 온갖.

Another example is 엊그저께, which originally was a combination of 어제 (yesterday) and 그저께 (the day before yesterday). So, the 엊 part of 엊그저께 is a result of the ㅔ in 어제 being dropped, leaving just ㅈ, which is then added to the 어 to form 엊, and that results in 어제그저께 becoming 엊그저께, which means "a few days ago."

Which is correct: 걸맞는 부부 or 걸맞은 혼인?

ANSWER: 걸맞은 혼인 is the correct phrase, which can translate as "a well-met marriage." So, what is wrong with saying 걸맞는 부부? Well, 걸맞다 is an adjective, not a verb, and adjectives modify nouns and pronouns by using ㄴ/은, not 는. So, 걸맞는 부부 should be 걸맞은 부부, which translates as "a well-matched married couple." My dictionary seems to have made a mistake.

What's the difference between 궁색하다 and 군색하다?

ANSWER: One means "poor," and the other means "really poor." Also, one of them can also mean "awkward."

My Korean-English dictionary does not really show much difference between 궁색 and 군색, but my Korean-Korean dictionary defines 궁색 as "아주 가난함," which translates as "very poor," while defining 군색 as "필요한 것이 없거나 모자라서 어렵고 답답함," which seems to essentially translate as "needy." Also, my Korean-Korean dictionary shows a second definition for 군색, which is "자유롭거나 자연스럽지 못하여 거북하고 어색함," and that essentially translates as "awkward."

Anyway, when Koreans talk about someone being "poor," they seem to use 궁색하다 much more than 군색하다, but when they talk about "an awkward excuse" or "a lame excuse," originally the only correct phrase was "군색한 변명," not "궁색한 변명."

Donga's Prime Korean-English Dictionary (1998 edition)