Seems / I heard
Endings that show where your information comes from: what you see, what you infer, and what you heard. All four share one base sentence.
-sou
polite -sou desulooks (like it'll be)
〜そう 〜そうです
Says how something looks right now, before you know for sure (oishisou). On verb stems it means something is about to happen (furisou = looks like rain).
kono keeki oishisou
This cake looks delicious.
このケーキおいしそう
kono keeki, oishisou desu ne
This cake looks delicious, doesn't it?
このケーキ、おいしそうですね
It attaches to the stem (oishii → oishisou); the irregulars are ii → yosasou and nai → nasasou. It is not for what's plainly visible: a red car is akai, not *akasou. kawaisou means 'poor thing', not 'looks cute'.
mitai
polite mitai desuseems / looks like
みたい みたいです
Says something seems so, either from what you see yourself (dare mo inai mitai) or from what you've heard (oishii mitai da yo). It is the everyday catch-all; rashii is a bit more detached. It also means 'like a' (kodomo mitai, kodomo mitai na hito).
kono keeki oishii mitai
This cake seems to be good.
このケーキおいしいみたい
kono keeki, oishii mitai desu yo
This cake's supposed to be good.
このケーキ、おいしいみたいですよ
No da before it: ame mitai, not *ame da mitai.
tte
polite sou desuthey say / I heard
って そうです
Ends a sentence to pass on what someone said or what you heard (ashita ame da tte). It attaches to the plain form and keeps da after nouns.
kono keeki oishii tte
They say this cake is good.
このケーキおいしいって
kono keeki, oishii sou desu yo
I hear this cake is good.
このケーキ、おいしいそうですよ
Polite oishii sou desu (I hear it's good) and oishisou desu (it looks good) differ only in the i. Also very common: oishii tte kikimashita (I heard it's good).
rashii
polite rashii desuapparently / I hear
らしい らしいです
Passes on secondhand information you believe but didn't witness, with a little more distance than mitai or tte. No da after nouns (ame rashii).
kono keeki oishii rashii
Apparently this cake is good.
このケーキおいしいらしい
kono keeki wa oishii rashii desu
Apparently this cake is good.
このケーキはおいしいらしいです
Directly after a noun it can instead mean 'typical of' (otokorashii = manly).