The Goths (actually two separate peoples, the Ostrogoths and later the Visigoths) , as with the Huns moved into central and southern Europe from the Steppe - not Germany - towards the end of the Roman Empire (the Visigoths sacked Rome on 24 August 410). They weren't Germanic, unlike the Angles, Saxons and Jutes that moved to / invaded the land of the Britons, and even tribes like the Francs who moved into Gaul as the Western Roman Empire lost influence.

I think you're right about the use of Viking being early, but some of the other elements differ from my understanding.

Two awesome sidebars from that period - another Germanic tribe, the Vandals, wrought havoc moving through what would become France and Spain. And a tribe of Scots were forced from their ancestral home ... in modern day Ireland. They replaced the earlier Picts in the land ultimately named after them.

[Edit: Corrected the Sacking of Rome date - I was out by 2 weeks. So worth clarifying that this is from my memory of university history courses, not a fact-checked review.]