1. 에 and
Although they are different from each other, they sound almost the same practically.
We do not differentiate them that much.
2. 어 and 오
They are definitely different from each other.
Think about an English word 'or'.
Though 'r' is a consonant, it sounds to me '어' in Korean.
When I hear the word 'or', I could transliterate it as '오어' in Korean.
Listen and practice 오/어 everyday.
에 and 애 are homophones. They are not pronounced any different. Trust me.
You use 에 after a location so like 학교에 means "at school" while
애 is used for everything else. That is the general guideline when you need to use 애 or 에.
As for 어 and 오. You tend to hear 어 in the middle of the sentence and 오 is typically at the end of the sentence.
These are not homophones.
어 is uh
오 is oh
This is what my teacher told me, and it worked for me. In fact, it worked for everyone I know.
에 = E as in BED
애 = A as in BAD.
In reality, native Koreans will not know difference - at least not consciously. When the time came, I saw that every single native Koreans cold tell the difference. So if someone say they are exactly the same, don't believe them.
어 = Awww
오 = Ohhhh.
That's all you need to know.
In reality, Koreans will get lazy and may not pronounce these vowels precisely. We learn to recognize these "accents" as we become more proficient. You need not to worry about it now if what you are studying now is Hangul.