Some of the designs of the homunculi seem fairly obvious and others not so much. I'll try to weigh in with some of my own thoughts and I'll also reference the trivia sections from the wiki pages for each homunculus when there is something relevant there.
Envy's appearance as a giant green monster seems to be a reference to the idioms "green with envy" and "green-eyed monster" (I've also heard this as just "green monster" or "little green monster", which are more appropriate for Envy). Envy's ability to transform into other people seems fitting since an envious person would want to be the person they are envious of.
This one seems fairly obvious. Her appearance is that of a voluptuous woman with wide hips and slender waist, usually immodestly garbed. She's an embodiment of lust.
This is another obvious one. Gluttony's obesity is a result of engaging in gluttony. His large mouths facilitate his gluttonous eating habits.
Since he's very proud to be the first of Father's homunculus, it makes sense that he takes a form similar to Father's first form. His wiki page also suggests that the many eyes on his shadow may be reminiscent of a peacock's tail and a peacock is a symbol of pride. The wiki page also notes that his humanoid container being a child may be a reference to the word homunculus literally meaning "little human". In this sense, he is sort of the closest to being a true homunculus (looking separately at the Fullmetal Alchemist definition for his shadow form and the real world definition for his humanoid container) and he's proud of it.
Wrath's appearance is that of a middle-aged man with an eye-patch. It's a little difficult to determine the connection to wrath. Wrath does often have a fierce scowl and perhaps his role as dictator and military attire help him personify wrath.
Sloth's appearance is perhaps the most difficult to explain. He's large and muscular, which seems to be at odds with his slothful nature. I don't have an explanation for it. His big nose does remind me a little of the animal sloth.
His appearance is that of a typical human both in his first and second bodies. According to his wiki page, Greed sharing a human body with Ling could be a reference to Dante's Inferno, where the greedy are always having their bodies stolen from them by lizards and they have to steal a human form from another sinner (Interestingly, all the homunculi have some connection to Dante's Inferno. None of the other points are relevant here, but you can look through the trivia sections on their wiki pages if interested). This also accounts for why Greed just has a normal human form. I have no explanation for his appearance when using his ultimate shield.
In your question, you ask whether there might be common image for these characters in Japanese folklore. I don't know much about Japanese folklore other than what little information I've gleamed from anime and manga, but I think it is probably unlikely. This is because the seven deadly sins come from Christian theology (see Wikipedia for details).
Wiki pages for Wrath, Lust, Gluttony, Greed, Sloth, Envy, and Pride on http://fma.wikia.com/
Seven Deadly Sins on wikipedia.org