As you know, all three grammar points roughly all convey the meaning even though or even if. The difference between -아/어도 and -더라도 is that 더라도 is used in more hypothetical type situations. So if you compare
- 수지는 화나도 욕을 안 할거야
- 수지는 화나더라도 욕을 안 할거야
The difference is that in the second example there is emphasis on “EVEN if Suzy were to become angry she wouldn’t swear”. It sounds more hypothetical, and the chance of happening is less. Because 더라도 is used in hypothetical situations that haven’t actually happened yet, you can’t use this pattern for the past tense. (했더라도 is fine, the second clause can’t be in past tense).
Using 어/어도 is the most flexible and generalized. There is no overly strong stress on the condition, nor is there any condition imposed on the tense you can use. So you could say 화나도 욕을 안 했어/해/할거야.
Note that 더라도 is fine for present tense usage as well:
- 비가 오더라도 학교에 꼭 가
- 일이 힘들더라고 가족을 생각하고 해야돼
- 조금 비싸더라도 품질이 좋으면 살 만 해 (even if its expensive, if the quality is good its worth buying)
-아/어도: Can be used for any tense and is the more general expression
-더라도: Can’t be used for past tense and the first clause is more hypothetical and less likely to happen. Used if you want to stress EVEN if the first clause is true/happens, it will have no bearing on the second clause.
Literally translates to ‘even if it is said that’, ‘even if you say that’. An example to highlight the difference:
- 아무리 힘들더라도 너는 끝까지 포기하지 말아야 한다. No matter how hard it is you must never give up
- 아무리 힘들다고 해도 너는 끝까지 포기하지 말아야 한다. No matter how hard it is said to be you must never give up
-다고 해도 is taught as a quoting grammar structure, but it is still fine to use this grammar when you are not literally quoting someone. It just gives the meaning of ‘even if it is said that’. Note that sometimes the 해도 can be omitted with no change to the meaning.
This grammar actually has another very common usage of “just because” that I discuss here. For example “just because you’re smart it doesn’t mean you’re always right”