[The Squatter of Amon Rûdh]

The Tolkien Studies blog is right about variag being hard to find in a dictionary. I have a complete Oxford here, and even in that it appears only in passing under varangian, in a section of the Dictionary that I believe was being compiled while Tolkien was employed there.

In the old Russian chronicle of Nestor the name [varangian] occurs as variags and variazi (pl.) and survives in mod. Russ. варигь a pedlar, Ruthenian varjah a big, strong man

The OED goes on to say that Partington's British Cyclopædia of Literature identifies the Varangians as "a race of bold pirates who infested the coasts of the Baltic".

It's possible that Tolkien intended to convey the sense of a mercenary or pirate. What I find very interesting is that he chooses to use a specifically Russian word for people who originated in Scandinavia and north-western Europe. The Scandinavian origins of the Rus are well known, so it may be that he wanted to imply a branch of the northern peoples that included the Rohirrim. Possibly he intended to imply in one word a group who were akin to but long sundered from the people of the North, living in Khand but not originally native to it, perhaps employed as swords for hire and now seeming foreign to their close relatives elsewhere. It's also possible that he liked the sound of the word, or thought it carried overtones of menace. The overall effect, though, is to give a thoroughly alien feeling to the otherwise reasonably familiar Varangians. Tolkien often also uses synonyms for 'pirate' as names for groups aligned with Sauron (or at least against Gondor), cf Corsair, although I have a suspicion that he might have taken exception to Partington's vague definition. With Tolkien, any, all or none of my suggestions might be true, and I am thinking aloud so to speak, so I may be far off target. It would be very like Tolkien, though, to use a word with the intention that his readers would immediately see - as he did - various layers of historical meaning and significance. He was particularly fond of a terseness of diction that packs a great deal of meaning into few words, and this is one way to achieve that effect. Also, in my view, more often than not JRRT overestimates the average learning of his audience (certainly in my case): one of his more endearing traits.