と聞(き)いたI heard that

ようだ expresses that something appears a certain way, based on various cues that are not always explicitly stated, e.g. 雨が降るようだ ('It seems it will rain.', perhaps because people are carrying umbrellas, etc.). In contrast, ときいた specifically means 'I heard (A)', and indicates that the information is hearsay directly obtained by the speaker.

Both ときいた and んだって express hearsay, but with different nuances and formality. 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, んだって is casual and adds an explanatory nuance, like 'They say (A).' or 'I heard that (A).', e.g. 高いんだって ('They say it's expensive, you know.').

らしい ① and ときいた both convey information obtained from another source, but with different nuances. らしい ① expresses hearsay, with the nuance that the speaker is relatively confident about the information, e.g. 雨が降るらしい ('Apparently, it's going to rain.'). In contrast, ときいた literally means 'I heard (A)', with no implication about the speaker's belief, and it cannot be used for information obtained from e.g. written sources.

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 ときいた and だって express hearsay, but differ in tone and formality. ときいた means 'I heard that (A)' and is neutral and conveys information directly heard by the speaker, while だって is casual and emphatic, often used in conversation to mean something like 'They say (A).' or 'I'm telling you (A).'.