One of Krause's theories is that the word Erilaz, which appears in a small number of inscriptions, had a meaning of "Rune Magician". This was taken further by Thorsson, who postulated a cult or guild of rune magicians connected with a tribe called by the Romans "Heruli".
There are about a dozen early inscriptions of the form "I the Eril, wrote this" (-az being the masculine singular word ending). There is no indication in the inscriptions that gives a clue to the meaning of the word. However, there is fairly good linguistic evidence.
It is accepted by many scholars that there is a linguistic link between the name of the Germanic warriors listed by the Romans as "Heruli", the "Erilaz" from the runic inscriptions, and the Old Norse "Jarl", Old English "Eorl", and modern English "Earl". However, there is still much debate and disagreement among the experts, many do not accept that "Erilaz" has anything to do with the actual groups called "Heruli".
If we look at the linguistics, the only viable theory connects all of these words to warriors or armies. The reconstructed Germanic root is "*Harjaz", = army. The word survives remarkably little changed in modern English as "to harry", a term still used in the military to describe repeated surprise attacks designed to wear the enemy down, or test their strength. It also survives in German as "Heer" = "Army". It is also the root word of the warriors of Valhalla, the "Einherjar", and of names such as "Hereward" (army-protector).
The Jarl or Earl was originally the leader of an army. The Heruli were "the army people", "those who harry", or "the marauders". "Ek Erilaz" almost certainly meant "I the warrior". The word obviously had a lot of prestige, and this is not surprising in a culture that valued warriorship so highly. The word gained further in prestige until it meant "army leader" (Jarl/Earl). There is a clear linguistic theme in which the meaning of the root word remains consistent. It is highly unlikely that such a word would have changed meaning so radically that it ever suggested "rune magician" at any stage.
There is mention in the Rigsthula that a Jarl should be an educated person, who should know runes and also magic, among a many other things. It can not be interpreted as saying that a Jarl was a rune magician, merely that an ideal Jarl should be broadly educated. Warriorship was still the Jarl's primary business. Virtually all other sources place Jarls squarely in their military and political occupations.
Nothing in the linguistic or historical evidence suggests "Erilaz" means "rune magician". In fact the bulk of evidence points against it. The most widely accepted meaning of "ek Erilaz" is "I the Earl", indicating a warrior of high standing or a commander who is stating his authority.
Proto Germanic reconstruction (dating before 100ce)
*Harjaz = "Army" (cognate with German Heer = Army)
*-il- = "person belonging to" (cognate with English -ling ) Example: Earthling
*Harjilaz = "Army Person" = Warrior
Note 1: Cognate words = directly related in form, meaning, & history.
Note 2: that j is pronounced as a y as in English "yes" (or the J in German "Ja")
Eg. Har-yaz. Har-yil-az.
Roman: Heruli, Greek Eruloi (dating from around 250ce onwards)
Runic: Erilaz (dating from around 200ce - 400ce)
Old Saxon - Erl - Man, Warrior
Old English - Eorl - Warrior Leader, Noble
Old Norse - Jarl - Warrior Leader, Noble
Modern English Earl - Noble Rank
All of these refer to warrior nobility and military leadership.
*Harjil- .. Heril- .. Eril- .. Erl .. Eorl/Jarl .. Earl
Army Person - Warrior - Warrior Leader - Leadership/Rank/Nobility
When the Romans asked the raiders "what do you call yourselves?", They would have answered "the warriors" Heriloz (plural of Herilaz). A common effect in the phonology of words with such endings is that the preceding vowel is conditioned by the vowel in the ending as it changes. This would have caused lowering and rounding of the i as the ending changed from "-az" to "-oz" (singular to plural).
This conditioning of the unstressed i would have made it sound like a u, making Heriloz sound like Heruloz. Hence the Romanised "Heruli" rather than "Herili".
The initial h in *harjaz was never dropped (eg. Heer), most likely because there were other words that needed to be distinguished from it by the h. Dropping it would have caused it to sound like another existing word. However, with Herilaz, there were no competing words. In this situation an initial h often becomes optional.
Erilaz is often transcribed ErilaR. The final R indicates a transitional period as the Germanic final z evolved into the Old Norse final r.