These three all mean something close to 'seems', separated by what the impression rests on: そう on what you see, よう on inference, みたい on a casual resemblance.
Also known assou you mitaiそう よう みたいseems like japaneselooks like
A judgement from appearance: い-adj drop い + そう, verb-stem + そう.
いまにも あめが ふりそうです。
It looks like it's about to rain any moment.
い-adjectives drop い (おいしい→おいしそう), な-adjectives drop な (元気→元気そう), verbs use the ます-stem (降ります→降りそう). It reports an impression from what you see.
Irregular: いい→よさそう, ない→なさそう. This そう (appearance) is different from the hearsay そう in lesson 47.
In the textbooksMinna II, lesson 43
A conclusion you infer from evidence: 〜ようです.
だれか へやに いるようです。
It seems someone is in the room.
ようです expresses a guess based on what you observe (sounds, traces, your senses). It attaches to the plain form; na-adj/noun add な/の (静かなようです, 病気のようです). Casual: 〜みたい.
In the textbooksMinna II, lesson 47