About how many years passed between the time the Germans first settled in the Roman Empire, and the time when Odoacer took control of it?
The first Germans to enter the Roman Empire did so around AD 166. Odoacer was proclaimed king in 476 AD after he defeated Orestes at the city of Piacenza. Approximately 310 years passed between the first entrance into the Empire and Odoacer becoming king. Odoacer is considered the first king of Italy and his reign marked the end of the Western Roman Empire.
The first Germans entered in 166 AD asking permission to settle. They were refused and pushed back. During the next ninety years, various conflicts raged along the border until 256 AD when the Romans abandoned Dacia for German settlement by the Visigoths. Throughout the next few hundred years, there was little peace between the various German tribes (Huns, Visigoths, Ostrogoths) and the Romans until the rise of Odoacer in 476 AD.