It seems you have started quite the discussion with a few simple questions. Great things are often wrought this way, and you will frequently wind up with a whole lot more information than you were originally seeking. I believe this qulaifies!
I thought some simple definitions might be helpful to you, in your quest for knowledge. I hope I'm not overstepping my bounds, but I'm certain that if I get something wrong, somebody will correct me, so here goes. I am writing this from ground zero, as I don't know how much of this you know already, so please do not be offended. That is definitely NOT my intent.
The roster of Al Khamsa horses was begun using the Blue Arabian Horse Catalog as a foundation. The BAHC was so named because (as legend has it), Ms. Ott kept her information and research notes, etc, in a notebook with a blue cover. All the horses in that book are Blue List. Some, those without recorded Mun'iqi Strain, are BLUE STAR (with the horses' names capitalized to differentiate them at a glance), and some are "sub-listed", which is a bit like an Honerable Mention.
Al Khamsa has added to the original roster as they feel necessary, based on extensive research and a two-part voting process. A horse has to be voted in twice to be added to the roster. These horses are listed in the Al Khamsa Arabians books, which is presently only complete to 1998. Al Khamsa Arabians III is in the works as we speak. I am typing this with AK II in my lap for reference, so it should be right on the money.
In these books AK recognizes a defined set of ancestral elements., and next to each horse's name in the roster there is an abbreviation stating which of these elements a given horse carries. The most common ones are:
Blunt: refers to horses obtained by the Blunts from sources other than Egypt.
Egypt I and II: refers to the foundation stock imported into and used for breeding in Egypt over a period of roughly 90 years. Because of the huge timespan this covers, it is divided into two parts. Egypt I - horses imported before the founding on the Royal Agricultural Society in 1914. Egypt II - horses imported after that date.
Inshass: The former kings of Egypt, Fouad and Farouk, maintained the Inshass stud as their personal enterprise. Their foundation breeding stock was comprised of horses of established Egyptian bloodlines, horses they acquired for racing and breeding, and horses that were gifts from the Sa'ud studs in Saudi Arabia.
In the interest of keeping this message to a manageable lengh, I will simply list the rest, and let you go to the Al Khamsa web site for their definitions. Also, I don't know NEARLY as much about these, so will leave it to those more knowledgable to fill in my gaps.
DAVENPORT, SA'UD, AYERZA, BORDEN, CAVEDO, COBB, CRANE, DWARKA, HAMIDIE, HUNTINGTON, JILUWI, KHALIFA, MIRAGE, NEJDRAN, RICHARDS, TA'AN,
their basic definitions can be found at http://www.alkhamsa.org/ancelements.html
At any rate, you asked what Heirloom and Sheykh Obeyd are. Simply put, horses that trace ONLY to Egypt I and Blunt ancestral elements are Heirloom. Horses that trace ONLY to Egypt I, Egypt II, and Blunt ae's are Sheykh Obeyd. As far as Pyramid Society Straight Egyptian goes, it is possible for a horse to be "Straight Egyptian" and not be Al Khamsa. There are also horses that are Al Khamsa, Blue List, AND Heirloom that are not PS eligible.
What a head-spinning thing this horse-breeding and history stuff can be, eh? Hope I didn't add to the fire. I'll keep my mouth shut now, and let the more experienced people do the talking.
Have a wonderful day!