"Female" can refer to any living thing that has two sexes. It is a neutral word, free from cultural overtones.
"Oh, what a cute little dog. Is it a 'he' or a 'she?'" "She's female."
"The male peacock is brightly colored, the female peahen is drab."
"Many plants have complete flowers with both male and female parts, others only have male or female parts, and still other plants have flowers on the same plant that are a mix of male and female flowers.
"Woman" simply means a female human being. "Lady" is a respectful term for a woman. Because "lady" is respectful, by contrast "woman" is sometimes seen as slightly disrespectful. When in doubt, say "lady."
"Girl" is VERY COMPLICATED. The simple literal meaning of the word is "female child."
"Girl" can be a disrespectful term for a woman. In the 1950s it was common to call female office workers "girls," meaning that, like children, they did not have equal status with the male workers. "I'll have my girl type that up for you..."
"Girl," oddly, can be a term emphasizing sexuality. This may be because in human courtship people play at being childlike. In the song from the musical "Flower Drum Song," a woman says she likes acting sexy: "I'm a girl, and by me it's only great/I am proud that my sihouette is curvy/That I walk with a sweet and girlish gait/With my hips kind of swivelly and swervy."