Neither of these words is used very often. Nonetheless, even if you haven’t seen either at all, I suspect you’ll have a sense of the meaning. And yes, they both mean largely the same thing. If I give you a sentence context you’ll understand the general intent. Here are a couple of quotations, obligingly supplied by the Oxford English Dictionary:
Zevon has built a career on well-crafted pop songs that tend to be either smartass and sensitive or smartass and skeevy. (Newsday, 1991)
He has the requisite erotic credentials—drugstore musk cologne, underarm sweat rings, skeezy tattoo, outer-boroughs grammar. (Los Angeles Times 1995)
Words like this are conditioned by phonetic profiling: what else they sound like. And what do they sound like? They both start with the /sk/ that is found on extensive and/or displeasing two-dimensional things: sky, skin, sketch, scum, scab, skank; they also have elements of sleazy, peeve, skivvies, skive, wheeze, sketchy, cheesy, easy, skeeter, and – for comic strip fans – Skeezix, a character supposedly named with a word for a lost calf, but it seems that the word skeezicks (the closest real-world spelling) was actually generally used to mean ‘rascal, rogue’.
So these words fall in line with sketchy and sleazy and skanky, with that thin wheedling /i/ vowel (which works well with pulling your mouth wide and the corners a bit down in revulsion), the fuzzy buzzing /v/ or /z/, and that hard, flat /sk/ onset. Were they just made up out of thin air because they sounded right?
Not quite. It starts with Italian (Tuscan) schifare ‘loathe’ and schifo ‘disgust’. Note that sch in Italian is pronounced /sk/, and in some versions of the language an f between vowels is said /v/ (a common transformation that, a millennium ago, was also the rule in English). These, at least in South Philadelphia, were borrowed over to English – quite possibly abetted by the sound resemblance to words of similar sense – to become skeevy, which was attested in print by the mid-1970s. Once that word became widely known, it was expectable that it would be modified to match the sleazy echo, especially since /izi/ endings are more common than /ivi/ ones in English. And, after all, this is an expressive word, with a sound-sense relation that is not seen as altogether arbitrary, so it’s more natural to change the sound to match what you feel. So by the early 1990s, we had skeezy, which is also a bit easier to say: you just take the tongue back to the tip, no need to involve the lips.
Is there a real difference between skeevy and skeezy? Aside from the one sounding closer to, say, evil and the other sounding closer to, say, easy? Well, Oxford adds “disreputable or immoral, esp. sexually” to – can you guess which? – skeezy. But dictionary.com specifies “not respectable; immoral” on… skeevy. Both agree that skeezy is sleazy, but Oxford says skeevy is too. Frankly, the whole thing seems a bit too… nebulous… you know… um, shady.