Gerunds (nouns + ing) and Possessives and Interpretations

Usually, when a noun or pronoun precedes (comes before) a gerund (verbal noun), it is logical to have that noun or pronoun take a possessive form. This is especially true in formal, academic writing.  However, this practice is restricted to pronouns and proper names.

In general, the possessive form (my, Marianne’s) is more literary and elegant. The objective form (me, Peter) is informal and used in normal conversation or writing especially after a verb or preposition.

Do you mind my opening the window?  (my = possessive, formal)
Do you mind me opening the window?  (me = object, informal)

He was annoyed by my smoking. (my = possessive, formal)
He was annoyed by me smoking. (me = object, informal)

They liked our singing. ( our = possessive, formal) = They liked our way / manner of singing,
They liked us singing. (us = object, informal) = They liked to listen to /hear us singing.

The teacher insisted on our speaking English. (our = possessive, formal)
The teacher insisted on us speaking English. (us = object, informal)

I hate their talking like that. (their = possessive, formal) = you hate when they talk like that but you don’t hate them
I hate them talking like that. (them = object, formal)  = either you hate them or you hate them for talking like that

Of course that depended on his finding a way to do it. (his = possessive, formal)
Of course that depended on him finding a way to do it. (him = object, informal)

I disapprove of his marrying my sister. (his = possessive, formal) = you disagree or think it’s a bad idea that he wants to marry your sister.
I disapprove of him marrying my sister. (him = object, informal) = either you disapprove of him or you disapprove of him because he wants to marry your sister.

I can't stand his singing (his = possessive, formal) = I like him but I don’t like the way he sings
I can't stand him singing. (him = object, informal) = either I don’t like him or I don’t like him when he sings

I noticed your standing in front of the police station. (your = possessive, formal) = I noticed how you were standing or your particular stance  (emphasis is on the standing)
I noticed you standing in front of the police station. (you = object, informal) = I noticed you and that you were standing (emphasis is on the person)

Do you think it’s right my, your, his, her, our, their eating meat? (possessives, formal)
Do you think it’s right me, you, him, her, us, them eating meat?  (objects, informal)