そうだ I heard that, It is said that

Both convey hearsay, but differ in tone and formality. そうだ is used to directly pass on something you've heard, e.g. 明日は休みだそうだ ('I heard he has tomorrow off.') ということだ is more formal and often sounds more confident or declarative. It can also carry a nuance of explanation or conclusion, e.g. 明日は休みになるということだ ('So that means / They say we'll have tomorrow off.')

らしい ① and そうだ both convey information heard from another source, but with different nuances. らしい ① suggests hearsay with some degree of certainty, implying the speaker believes it to be true, e.g. 'Apparently it's (A)'. In contrast, そうだ is more neutral, simply meaning 'I heard (A).' or 'They say (A).'. They also connect differently to nouns and な-Adjectives, e.g. 大変らしい vs. 大変だそうだ (both meaning 'It seems difficult.').

Both ときいた and そうだ express hearsay, but with different nuances. ときいた means 'I heard (A).' and conveys information directly heard by the speaker, e.g., 高いときいた ('I heard it was expensive.'). In contrast, そうだ reports hearsay in a more abstract fashion, similar to 'They say (A).' in English.

Both express hearsay, but with different tone and usage. んだって is very casual, often used in everyday conversation, and carries an explanatory tone due to んだ, e.g. 明日休みなんだって ('They said tomorrow's a day off, you know.') そうだ is more neutral and indirect, with no explanatory nuance, e.g. 明日休みだそうだ ('I heard tomorrow's a day off.')

といわれている and そうだ both report something heard, but differ in nuance. といわれている is more general and formal, e.g. 'It is said that (A)'. On the other hand, そうだ often implies someone specific said it and is more casual, e.g., 雨が降るそうだ ('I heard it's going to rain.').

Both can relay hearsay, but with different levels of certainty. とか adds a nuance of vagueness or uncertainty, e.g. 来月引っ越すとか ('I heard they might be moving next month, or something.') そうだ also conveys hearsay, but with less ambiguity, e.g. 来月引っ越すそうだ ('I heard they're moving next month.')

Both forms express observations similar to 'seems' or 'appears', but differ in nuance. そうだ is based on sensory clues, e.g. 雨が降りそうだ ('It looks like it'll rain.', because the sky is dark and the air is damp). ようだ is based on more concrete information or experience, e.g. 雨が降るようだ ('It seems it'll rain.' because people are carrying umbrellas, or the weather report said so).