~어/아서

• When the second clause is sequentially dependent on the first clause

• 슈퍼에 가서 장을 본다. "I go to the supermarket and buy groceries".

• In this example, you can't buy groceries before going to the supermarket. Thus, they're order dependent.

~다가

• When the action in the first clause is interrupted by or shifts to the action noted in the second clause. They aren't necessarily sequentially or causally related.
• 저전거를 타가다 넘어졌다. "I was riding my bike and I fell".
• In this example, the action of riding was interrupted by the act of falling. However, the two actions are not causally related.
• Do note that the action also doesn't necessarily have to completely stop.
• 잠을 자다가 무서운 꿈을 꿨다. "I was sleeping and had a scary dream".

~었/았다가

• Used similarly with ~다가 in terms of shifting actions. However, unlike ~다가, the action in the first clause completes before shifting to the second action.
• The clauses should also contrast or be opposites to each other.
• 셔츠를 샀다가 마음에 안 들어서 환볼했다. "I bought the shirt but then returned it because I didn't like it".
• In this example, there isn't an interruption but rather two contrasting situations. Also, the action of buying a shirt finishes before the return is made.

Some other things to note:

• In all three connectives, the subjects of both clauses must be the same.
• ~다가 and ~었/았다가 can be written without 가: ~다 and ~었/았다

~어/아서

• When the second clause is sequentially dependent on the first clause

• 슈퍼에 가서 장을 본다. "I go to the supermarket and buy groceries".

• In this example, you can't buy groceries before going to the supermarket. Therefore, they're order dependent.

~다가

• When the action in the first clause is interrupted by or shifts to the action noted in the second clause. They aren't necessarily sequentially or causally related.
• 저전거를 타다가 넘어졌다. "I was riding my bike and I fell".
• In this example, the action of riding was interrupted by the act of falling. However, the two actions are not causally related.
• Do note that the action also doesn't necessarily have to completely stop.
• 잠을 자다가 무서운 꿈을 꿨다. "I was sleeping and had a scary dream".

~었/았다가

• Used similarly with ~다가 in terms of shifting actions. However, unlike ~다가, the action in the first clause completes before shifting to the second action.
• The clauses should also contrast or be opposites of each other.
• 셔츠를 샀다가 마음에 안 들어서 환볼했다. "I bought the shirt but then returned it because I didn't like it".
• In this example, there isn't an interruption but rather two contrasting situations. Also, the action of buying a shirt finishes before the return is made.

Some other things to note:

• In all three connectives, the subjects of both clauses must be the same.
• ~다가 and ~었/았다가 can be written without 가: ~다 and ~었/았다