So here’s the thing, you have constructs that mean slightly different things all lumped together.
Noun + のようだ = In the manner of Noun
学生のようだ = Is like a student
Verb (generally past I believe) + ようだ = Appears that Verb has happened
彼は映画を見たようだ = He appears to have watched the movie
Adjectives aren’t generally used with this. This can be used in written sentences and non-casual speech.
Noun + みたい = Looks like Noun
学生みたい = Looks like a student
This is basically the casual version of ようだ and while I think you could use it with verbs as well, it’s mostly used with nouns. There is a slight nuance in that みたい focusses more on appearance and is seen in constructs where the subject isn’t supposed to normally “look like” that. Example a guy wearing a dress being called 女みたい.
Now そう actually has two things to be aware of. This is the construct that is usually used with the STEM of adjectives to say “something looks like adjective”. Example:
そのケーキがおいしそうですね… = That cake looks delicious doesn’t it
However, そうだ can also be used when reporting things you have been directly told by other sources. In this case you would NOT be using the stems, and you would use the following rules:
Noun/Na Adjective (without な) + だそうです/だ
Verb/I Adjective + そうです/だ
彼は先生だそうです = I’ve been told he is a teacher
田中さんの娘は背が高いそうです = I’ve heard Tanaka’s daughter is tall
昨日山田さんがアイスを全部食べたそうです = I was told Yamada ate all the ice cream yesterday
And finally らしい is similar to the above version of そうだ except this tell the listener you weren’t directly told this information, but based on what you know this is what you believe.
その人は誰ですか？ = Who is that person?
山田さんの友達らしいです = I believe that’s Yamada’s friend (based off some other information)