As the above answers/comments show, you can divide usage of らしい, みたい and っぽい into two rough categories: ending and thereby modifying entire sentences, or attached to something within the sentence (usually a noun phrase) to create an adjectival phrase. In the below examples, the first of each set is at the end of an entire sentence (Z は女 ○), and the second is modifying just a noun (女 ○).
There is some overlap, which can be confusing:
- Zは女らしい(よ) = It seems/I hear that Z is a woman.
- Zは女らしい(人) = Z is womanly (a womanly person).
... but usually context will make one interpretation much more likely than the other.
The sentence-ending usages indicate that you are deducing what you say from something you saw, heard, etc. You are not in a position to make a definitive statement. The modifier usages are more about making judgment, and ARE in many cases definitive statements.
- Modifier Xらしい roughly means "fulfilling with ease the requirements for X", with a nuance of appropriateness or approval.
- Modifier Xっぽい roughly means "strongly evidences the characteristics associated with X", with a nuance of inappropriateness or disapproval.
- Modifier みたい comes originally from 見たよう and it simply means "appears to be, looks like, acts like, seems like". It does not require that the information be obtained visually, though: 赤ちゃんみたいな鳴き声, etc. X みたいな Y carries the implication that Y is not in the category of X.
- 女らしい would usually be applied to women, who are expected to be womanly, and 女っぽい to men, who are not, or to women who the speaker judges to be acting in a too stereotypically "womanly" way. (And both the "praise" and "blame" nuances can be used ironically, too... but this is a bit of a rabbit hole.)
- 彼女は女みたいだ is basically an inappropriate thing to say, because if you are calling her 彼女 you know that she is in the category of 女 -- you are essentially denying that she IS a woman, and simply saying that she looks/acts like one. This sort of sentence is used, though, as a sort of mock-insult among friends (for example, you might say 女みたい to a friend who is acting/dressed in a way you deem womanly even though she normally does/is not), but it can obviously backfire very easily.
Note: There is probably room for disagreement over how distinct these sentence-ending and modifier usages really are. For らしい at least, the "hearsay" and "appropriately" meanings are pretty distinct. For the others, you could maybe argue that both usages are fundamentally the same, with any perceived difference in meaning arising from context/function in the sentence rather than inherent semantic differences.