Unfortunately, I lack the expertise to give you an overview of daily life in Rome during the fifth century, I’ll leave that to someone more qualified like /u/shlin28. That said, I would like to offer some political considerations related to your question.

While Rome remained a large city and the cultural heart of Italy, it had ceased to be political relevant by the time of Odoacer. During the fourth century, Milan had served as the capital of the Western Empire, before Honorius transferred it to Ravenna in 402. Surrounded by swampland, it was seen as far more defensible, and it could also be easily supplied by sea. Ravenna was thus the political center of Italy during the fourth and fifth centuries, and it was from here that Odoacer, and Theodoric, his successor, ruled from, in theory subordinate to the emperor in Constantinople. So while Rome remained an important city from a cultural, historical, and economic standpoint, as a center of administration it was no longer politically relevant. That said, individual members of the Senatorial class continued to remain influential, due in no small part to their enormous wealth. They continued to be involved in Odoacer’s administration, and doubtless still had ties to elites in Constantinople.