It might be the result of common Germanic grounds, not necessarily lateral influence. I got the same when learning German - sentences like "das Haus ist rot" or "ich trinke Wein" are surprisingly easy to catch up from English. And after some time you start noticing patterns, that help you further.
The evolution of languages is fascinating. Circling somewhat back to the topic above: the difference between "dialect" and "language" is a complex subject just as most "speciation" debates in other evolutionary fields have a lot of hidden complexity. "Language" versus "dialect" versus "creole" doesn't have a lot of simple answers though historically that joke that "a language is a dialect with an army" tracks more than it doesn't which is why it is a good joke.
[1] https://en.wikipedia.org/wiki/High_German_consonant_shift
(What I find really funny is that some people show some sort of intuitive awareness of those regular sound correspondences, when dealing with closely related languages. I don't recall this among EN/DE speakers, but it's all the time among PT/ES ones: either joking "swap O with UE and you get Spanish" or "drop random consonants and you get Portuguese". Cue to "quiero una cueca cuela y un sorviete" pseudo-Spanish.)
Among the three you mentioned (language, dialect, creole), at least creole is well defined - it's the resulting evolution of a pidgin becoming a full-fledged language. At least in theory, because in practice we get partial creolisation and decreolisation of varieties.
There's definitely some similarity between the two Germanic languages, but the North and West Germanic languages had started to diverge by the point of Danelaw, though the Battle of Maldon does record the languages as being mutually comprehensible at that point.
And more importantly: I don't think there were a lot of sound changes triggered by Norse influence, and those are the most relevant factor behind mutual intelligibility. Some odd non-core vocab here and there is easy to skip, and still get the "rough" meaning of a sentence, and speakerers cannen sentencen still understanden, eben mit somes oddes endinges.
