I have always tended to pronounce a lot of word in my own way... either a more Swedish pronounciation on it... or a pronounciation which I think sounds "cooler" then how it is "supposed" to be pronounced, or I sometimes also mix between Swedish and English pronunciation rules on a word. Remember, this is just how I say it, does not mean that I am actually right in how they are or should be pronounced.
Like the word "Scythe"... it is suppoed to be pronounced sort of syth/sieth/sigh-th or something like that. But I always pronounced the c as a k... "Sky-th", First it was because that was how I thought it was supposed to be pronounced, but later when I found out the right pronunciation I still felt I prefered skyth... because it sounds... cooler... more... I don't know... brutal? Compared to syth atleast. The real pronounciation sounds like your just sighing, which is not very... dramatic.
So I am going to try and explain it, but it might be difficult because some ways of saying letters in Swedish does not exist in english, or is very hard to find a word where that particular sound exists.
Rasalhague: I will devide the word into what I think is the natural division of the word, "Ra-sal-hauge". So let's start with Ra. The R has no unusual pronounciation, maybe a little roll to it, but that is not necessarily necessary, so we will focus on the A here. For that A I use the Swedish "short A" pronounciation. If you take the english word "area", the way the last A (areA) is pronounced, that is sort of how I say the A in Ra. It basicly needs to end abruptly when you say it, a quick punch of the letter basicly. As for the "sal" part. The S and L are normal ones. The A, once again, is the short Swedish A, so the same applies here as in "Ra". So Rasal is sort of a quick sharp double punch of the A's. It's not a flowing part like how "rassle/rassel" or something like that would be, but rather a... connected staccato of Ra-sal. Atleast I think that's the right word to use, staccato. So, on to "hauge". Unlike the Rasal part, Hauge is actually a fairly soft and flowing word when I say it. Also each letter, with the exception of the E (which becomes silent), are pronounced. There is actually a English word which sounds exacly like how I say the Hau part, and that word is "how". So just say How and add a G at the end. "Howg". I think that the W at the end of "how" creates a U like sounding part if it... which is why to me it sounds just like how I say "hau". So sharp staccato on the A's in Rasal, and soft and flowing on Hauge. Ra-sal-howg.
Skjaldborg: When I say it the words get devided into two parts "Skjald-borg". It could also be devided into "Sk-jald-borg", because there does come a slight slight break between the K and the J, since the shift from the K to the J in the word is not compleatly natural for our mouths. All letters in this word is pronounced when I say it as well. For the Sk part, take the word "Skate", the way the Sk is pronounced there befor the A sound comes into play. The J a normal one really, like in "Jim", or how Y is pronounced in many english words like in "yes". The A is the Short Swedish A that I explained on Rasalhauge. L is a normal L as used in for example "hello". And the D is also a normal one, like the one in "had" etc. As for Borg. I have two ways of pronouncing it... depending on if I want to sound more English, or more Swedish. The English sounding one is the same as how you guys tend to say it, like in "Björn Borg", or the "Borg" from Star Trek. Since Borg is a word in Swedish (meaning "fortress" as said elsewhere), we have our own way of saying it. The G is pronounced like a J, so "Borj". You could also use the English Y as in "yes" if you want to, to make the same sound.
Drakøns: I devide this word this way, "Drak-øns". The D R and K use a regular pronounciation. It's the A that is different from how most English speaking people would pronounce it. Depending on how I want the word to sound, I will switch between the short Swedish A, or the long Swedish A. The short one is the same as previously explained. Where as the long Swedish A is pretty much the same as the A in the name "Mark". As for the øns. The N and S are normal. The ø I pronounce in two different ways, either just a regular O... or the Swedish Ö. Ö is a hard one... difficult to find words in English where this sound is used. Luckilly with the help of Internet I found two pretty good examples. "Bird" and "Girl". The way how the I (i) in those words get pronounced. You have to try and really listen to it and, then slowly filter away the three other letters from the word to find the Ö sound. I suggest removing the last letter first, then the second to last, and then finally the first letter.
Also... I compleatly agree with Carl Wrede here (heh... Wrede, a common way for Swedes to change a word so that it can easier be used as a last name, original word would be "Vrede" which means "Anger"). Drakøns is a very weired word, which seems to have just been though up out of the blue. Also, the øØ letter is not Swedish. It is a letter used by mainly the Danes and Norwegians, it is their version of the Swedish (German, Icelandic, etc) öÖ. As Carl said there seems to be no particular connection really with any particular Swedish word, except that parts of it is simmilar to the Swedish words for Dragon/'s (Drake, Draken, Drakar, Drakarna).
In Swedish we do use "Drak" in words... but it is only used combined with other words, never alone. It's used in the sence to put a "stamp" if you will on something, to show what it is and what it belongs to. We do that with a lot of words. Either we cut of part of the end of a word, or change the last few letters to something else, or heck even not change the word at all, and then stick another word on the back of it to get a new word with something connected to the starting word. For example "dragon/'s claw", we don't say "drake klo", we say "drakklo" ( dragon/'s claw), or "drakklon" (the dragon/'s claw). "Dragon/'s wings" -> "Drakvingar", "Human hand" -> "Människohand", "Computer screen" -> "Datorskärm".
If I look at the Drakøns with Danish or Norwegian eyes (with the help of Google Translate), it does not seem to make much more sence in the context of a millitary unit/army. Because "Drak" in Danish apperantly means "Drink", and in Norwegian it apperantly means "Drunk". Although... now that I think about it... that would maybe make some sence for scandinavians and FRR I guess... a long long culture of alcoholism... often ending in bloodshed...
Looking at ø with the same eyes, in Danish it means island, and in Norwegian it does not seem to mean anything.
Then looking at Drakøns with Swedish eyes (changing the Danish/Norwegian ø to the Swedish ö), the word I actually get out of it is "Draköns". Which to me would mean "Dragon Island/'s" or "Dragons Island/'s", refering to that it's an island called "Dragon/'s Island", and that something is belonging to it (the "Ö" means "Island", the N after the Ö denotes that it is "The" Dragon/'s Island/'s (so a name), and the S at the end indicates that something is belonging or is connected to it. For example "The Dragon/'s Islands wildlife" -> "Draköns djurliv", "The Dragon/'s Islands Vulcano" -> "Draköns Vulkan". So yeah... Drakøns/Draköns makes little sence when it comes to a millitary unit in Swedish as well.
And I agree with kargush, probably scandinavian-ized to make it sound scandinavian. Which I guess works sort of, even if you do dig into it.