In my attempt to lure you here, the title, like most online titles, is sensational and largely bullshit. I didn't 'learn' the greek alphabet. I did however memorize the upper case letters well enough to regurgitate them correctly and get 24 points added to my New Testament Final. Here is how...
1) Chunking
2) Irrational association (yeah, I made this term up...)
3) Loci castle (for harder projects)
Chunking
An accepted standard for most of our cognitive abilities is captured in the idea known as "The Magical Number 7." Basically, with some exceptions, most of us can only hold between 5 to 9 "things" in our short term memory. A way to hack this limitation is to "chunk" ideas together. Try to establish connections between objects that lump them together. I personally separated the letters into 5 groups based on there order. The creativity to how you do this is seemingly unlimited. This brings me to the next concept
Irrational Association
Gall founded the pseudoscience of phrenology, the study of the mind based on the shape of one's head. I memorized this instantly by imagining a man on a ball (ball...gall...come on), rolling on people's heads creating depressions and lumps. It may sound odd, but I'll never forget it. The more outlandish, the more likely you are to remember it.
Loci Castle
This technique is for the badasses only. The principle is that we can vastly improve our memory if we create mental structures, such as houses, castles, or routes we take to work, and create an image of the thing we wish to remember and place it somewhere in our mental structures. At the moment, I only have one and its the house I grew up in. I start at the drive way, if I want to remember Gall, I'd place his head-mauling activity where my mail box would be. If I established a path I take through my house that is consistent, I can place the letters of the Greek alphabet along the way in places that were important to me as a child. I could put Beta in the driveway, or Omega on my bed.
This loci idea can become the most powerful memory device you ever acquire if you work on it. I haven't.
If this kind of stuff intrigues you, check out "Moonwalking with Einstein."