To put it simply, kanji are just symbols that represent ideas. Japanese uses them as the primary building blocks for vocabulary words (nouns, verbs, adjectives), so they're crucial to learn. The only good analogue I can think of in English is the number system. For instance, 1 is a symbol that represents the concept of "one". People might pronounce 1 differently in almost every language, but the concept that it represents never changes, if that makes sense.
To use a Japanese example, 人 is the kanji for "person" and it's used in most words that deal with person-ness. Some simple examples:
人 by itself just means "person".
一人 is one+person, which means "one person" or "alone".
二人 is two+person. You can probably guess what this one means. Yep, "two people" or "couple".
日本人 is sun+origin+person. All together, "a person from where the sun originates", which we all know is Japan. So this one means "Japanese".
And here's a more abstract example:
人工 is person+construction, which means "artificial" (and it also looks like A.I. which is a fun little happy coincidence).
Hopefully some of that helps somebody out there.
Your description is spot on; good ear! It will normally be loosely transcribed as <ɯ> in IPA, which is higher and farther back in the mouth than the <u> of English and Spanish, and is made with the mouth more closed (an exolabial close back vowel if you appreciate the technical term). It appears in the vowel glide of Standard Chinese "e" 鹅 etc. as well as on its own in some Southern dialects, and in (East) Norwegian "mot" etc. I'm not sure what other languages have it, though.
夜・よる is just the temporal noun "night"
"good night" is an expression and would be translated to おやすみなさい
Oyasumi means "Please rest" which is practically "Good night." But good night is different from night.