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I answered to your analogous question for the present continuous, now I do the same for the past :).

First of all, as DaG already told you, Italians don't usually say:

Io stavo andando a casa

but only:

Stavo andando a casa

unless you want to emphasize the subject, for example (here io is stressed):

Io ho lavato i piatti, non tu, fannullone!

Regarding the imperfetto di stare + gerundio, it is more or less like the past continuous in English, it is used to describe an action that was occurring in the past when some other action happened, for example:

Stavo andando tranquillamente a casa in macchina quando, all'improvviso, davanti a me è sbucata (not completely grammatically correct but used) una volpe

or

Stavo andando tranquillamente a casa in macchina quando, all'improvviso, davanti a me sbucò (correct but used only in formal Italian) una volpe

The imperfetto is used for habitual actions:

Quando abitavo a Milano, andavo al lavoro in tram tutti i giorni

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