Who were the tribes that invaded western Europe after the fall of the roman empire

The Germanic tribes . In particular, the Vandals, Sueves, and Burgundians who invaded Gaul in 406. Among these there were The Alans, who were Iranian-speakers, not Germanic. They too were referred to as barbarians, as this term applied to all peoples who lived outside the empire, not just to the Germanics. The Alemanni, Germanics from southern Germany, took advantage of the mentioned invasion to take over northeastern Gaul.

The Germanic peoples who settled in Britannia in waves were the Angles, Saxon, Jutes and Frisians.
These peoples invaded during the Western Roman empire not after it. Their invasions precipitated its fall.