First, let's start off with Satan. Satan, from my somewhat-extensive knowledge, only makes one true appearance in the Old Testament (that bloody, sexual, violent part of the Bible- you know, before the Jesus parts?) and it is in the book of Job. From what I remember (and I'm trying really hard not to google it right now, omfg), God is the one that really does not come off very well in that particular book. Here, Satan is merely an adversary, not truly doing anything but questioning God (which in itself is a sin since God cast out Adam and Eve for seeking knowledge), whilst God begins to torture poor Job in order to prove that his followers would follow him always. Satan is rather passive, and has no true ill will- in fact, he is merely there while God begins to inflict pain after pain on poor Job just to prove a point. (This is actually part and parcel to the God of the Old Testament, as he was a violent, jealous God, and even killed a man because he tripped and accidentally touched the ark of the covenant). To continue, Satan here lives up to his name, as in the original Hebrew, the name simply means "adversary" and, to my knowledge, does not have any "evil" connotations that are contemporarily assigned to either of the three concepts.
Now, The Devil, on the other hand, is the root of all evil, as promulgated by Christianity. He forces you into sinning (thereby removing free will? #Food4Thought) and then punishes you after you die. As a former Catholic, I have a lot of experience of being told of "Hell" and the punishments the "Devil" will inflict on me if I do things I'm not supposed to, like lying, stealing, killing, masturbating, throwing away food, and talking back to mamá (I think most Chicanos have experienced that last one, tbh). In some forms, you could even call el diablo a children's boggle, as he is sometimes used as such, especially in Latin American cultures. Personally, being sent to the devil for spilling something or a little white lie is a bit excessive, but hey, no one asked me, so whatevs. He's even on a loteria card! So, this idea of the Devil has even wiggled itself into the popular culture. Of course, he's already been in several things; Doctor Faustus is an old story about a German doctor who makes a deal with the devil in exchange for his soul (poor guy ends up in Hell), and this ideas has had several adaptations, most notably by Shakespeare's contemporary Christopher Marlowe and Johann Wolfgang von Goethe, who wrote Faust. Don't get me wrong, they're great stories, and you should def go read them (or at least google them), but in these instances, the Devil seems to function in his core existence--to entice humans into sinning and then punishing them for it. This seems to work strangely, as the Devil then takes the blame for most of the problems, both the temptation and the actual sin, while God is portrayed as blameless, which is probably the point. It's interesting to note what this may say about society and religion and how they interact.
Now, Lucifer, is the interesting one. I'm not too sure on how one became the others, but the one that seems to be bastardized the most is probably poor Lucifer. In popular culture, the three are consistently portrayed as one entity, which is simply not true. Satan is not the Devil is not Lucifer, in every possible combination. Lucifer is the Roman God of the morning star (aka the planet Venus); Lucifer is latin and means "Lightbearer" and held no real connection to Satan, despite what Supernatural may tell you. While he has no true stories in the rich (coughplagiarizedcough) tapestry we call Roman mythology, he is nonetheless one of their figures. I, honestly, have no idea how the three concepts were conflated, but the Lucifer one makes even less sense to me, as it is completely out of the blue.
In all honesty, one can see how Satan became the Devil in a largely uneducated and extremely violent civilization such as medieval Europe and how it continued to travel, but the Lucifer bit always confused the living fuck out of me. Does any one know? I would actually love to discuss this, at length, since it is time, I feel, that we begin to pull of these shackles of folk belief and follow things to the root, and see how something becomes something else. So if you know, or think something, feel free to comment ot dropme a line. :)
I will think of you occasionally, anonymous peasants! :P