Pure hogwash. These guys are reviving apparently unchanged the arguments of an amateur linguist from the 1940s. You can see their 100 "best of" here. When these volumes were first published, one professional linguist called this work "an effrontery to American scholarship." It's difficult to enumerate the basic problems, so let's walk through an example.

The original author, Sherwin, was comparing phrases, not words. For example, he discusses Illinois, derived from Algonquin "illini wok," which means "real men." He then scouted for words with both similar meaning and sound. He settled on the phrase "decent people," which translated into an unidentified Norwegian dialect as "hreina foolk."

Obviously, there'd have to be some major changes to get "hreina foolk" to sound anything like "illini wok." These changes are possible perhaps, but it's important to recognize that languages change according to rules. For example, maybe the speakers of a language all adopt a lisp and "Barcelona" becomes "Barthelona." But these changes occur across an entire language, not just in individual words, so explaining the connection between "hreina foolk" and "illini wok" would actually require some serious comprehensive study, not just a superficial similarity of sound when you stuff your mouth with cotton balls.

But not only is Sherwin disregarding how sounds would need to change; his meanings diverge too. If "hreina foolk" and "illini wok" are indeed related, then how did "decent" (hreina) come to mean "real" (illini)? These words don't even mean similar things. Or how did "people" (foolk) come to mean "men" (wok)? And did this new word for "men" produce a back-formation singular for "man"? Old Norse has a perfectly fine word for "man" and "men," so why would another word acquire this meaning? Again, these changes can happen (like how we sometimes use the word "peep" derived from "people"), but it's a bit of a stretch.

So the basic problem is that, although Sherwin can find some similarities in sound between some phrases that mean similar things, he can't explain how either sound or meaning changed. (Let's not even touch the problem of whether Algonquin is grammatically similar to Old Norse.) Sherwin tries to get around this by claiming that he's referencing a particularly ancient dialect of Norwegian.

Contemporary linguists were unimpressed. Not only was Icelandic already accepted as the dialect most similar to Viking-Age Norse, but also it makes his work completely unverifiable. He never even identified who spoke this purported Norwegian dialect! So these blog claims rest on a basic ignorance about how languages work and are supported by unverifiable evidence. Hogwash indeed.

He just looked around for words in Norse to match the Native American ones. For instance, Michigan means "big lake", derived from michaa and -gami, a suffix meaning "lake". His construction is about as valid as saying it's derived from English "mid-chicken" because they sound similar.

Algonqian is also not one language, and it would take quite a while for any borrowings to diffuse throughout the whole language family (and somehow not undergo phonetic changes).