This is a great example of why Korean can be such a difficult language to learn! Each of these grammar points are used to clarify and confirm information from others, in slightly different contexts.
+다고요 ~ used to clarify by repeating what the other speaker has just said, ‘You said?’
Did you say you went to the US?
3년 동안 공부했다고요?
Did you say you’ve been studying for 3 years?
+ 다고 하던데 ~ used when recalling or confirming something you heard someone else say previously, ‘I heard’
아주 좋은 영화라고 하던데요
I heard it is a really good movie
오늘 춥다고 하던데 건강 조심들 하세요
I heard it is cold today so take care of your health.
+다면서요 ~ used when confirming with someone what you heard from another source, ‘Is it true?’
Is it true you and your girlfriend split up?
호주에는 지금 아주 덥다면서요?
Is it true that is is really hot in Australia right now?
+다니요 ~ used to express surprise or disbelief about what has been said, ‘Really?!’
It’s already midnight?
You got married!? Congratulations!
Tricky! Especially given all the different conjugations. 열심하 공부해요!