I am not familiar with Pryor's work, and while I know a bit about Oosthuizen's, I haven't read The Emergence of the English (her main book on the subject). The idea that there was no population movement from mainland Europe in late antiquity, or at least that such migration was not the main force behind the creation of Old English, is a small minority view. Calling the scholars who argue for it crackpots or cranks is going too far though.

When pressed on the question in interviews, Oosthuizen usually says something like 'I would be surprised if there was no migration,' so she doesn't even really subscribe to the idea that there was no population movement at all. What these scholars are usually trying to do is point out that there are a lot of flawed assumptions underlying the traditional understanding of Britain in late antiquity. I don't think the alternate theories they propose are likely correct, but they are technically also possible.

Many of the points they emphasize while making their arguments are also very good to keep in mind when studying the past in general.

• DNA is not identity
  • Just because we identify 60% or whatever of a skeleton's DNA as 'Germanic,' does not mean that that person identified with a Germanic ethnicity in life or spoke a Germanic language. Culture is not biological, and the idea that it is has a lot of really nasty implications in European history.
• Artifacts are not people
  • Just because an artifact that we identify as 'Germanic' is found somewhere does not mean that a person who identified with a Germanic ethnicity or spoke a Germanic language left it there. This can really be boiled down to 'trade and cultural exchange exist.' Invasion and migration are not the only explanations for a style of artifact showing up in a new area.
• Historical documents are not necessarily reliable
  • The idea of barbarian invasions remaking post-Roman Britain comes entirely from On the Ruin and Conquest of Britain, a text written by a British monk named Gildas in the 5th or 6th century. The problem with this is that Ruin and Conquest was never meant to be a history of post-Roman Britain. Most of it is actually a summary of biblical events. Gildas then draws parallels between this biblical material and claims about his contemporaries to make an argument that British society is sinful and bound to incur God's wrath. Ruin and Conquest is a sermon, not a history. It is written with a polemic agenda and can't be relied on as a source of historical fact. For all we know, Gildas could have been the Alex Jones of his day.

I've typed a stupid amount and still not answered your question: "where did the English language really come from?" The only honest answer is that nobody can say for certain. Anybody who tells you they can is kidding themselves. There is just too little good evidence. It was probably a much lengthier and more complex process than we will ever truly understand.

Now as I understand it, Oosthuizen's theory is that an ancestor to Old English was already spoken along the North Sea coast of Britain before the end of Roman rule. It could have been brought by earlier migrations and/or or introduced to Britain as a trade language by merchants traveling across the North Sea. As Roman influence receded, exchange across the English Channel and ultimately to the Mediterranean became less important to British society. To fill the void, trade across the North Sea became more important, and thus so did this pre-existing Germanic trade language along the North Sea coast. It became the lingua franca of a new economy and society integrated with the North Sea zone instead of the Mediterranean, and so over time whatever variants of Brythonic and Latin remained in what would become England were disfavored and eventually died out. In her view, this theory both explains the spread of Old English language and culture as well as the absence of archaeological evidence for some catastrophic destruction and replacement of Romano-British society.