How would I apply feminist criticism to The Picture of Dorian Gray given that Lord Henry constantly speaks about women as if they were simply objects.
As The Picture of Dorian Gray is social satire, you shouldn't put too much literal stock in anything anyone says. If you want to understand how the artist or Oscar Wilde feels about women, you should try to understand the very opposite of their words.
Lord Henry is a Vice figure, a Satanic hero, the sarcastic voice of the author. He's a mouthpiece for Wilde to pretend to be an elitist and sexist socialites of the time, and he's too unrealistic to be taken too seriously.
Lord Henry's epigrams are little zingers that are part of Wilde's wit and not meant to be realistic social commentary. The worst thing you can do is take them out of context:
My dear boy, no woman is a genius. Women are a decorative sex. They never have anything to say, but they say it charmingly. Women represent the triumph of matter over mind, just as men represent the triumph of mind over morals.
Men marry because they are tired; women, because they are curious: both are disappointed.
In an epigram everyone is treated like an object. They're all generalization and stereotype. That's the point.
Remember, an epigram is
a statement contradictory to what is accepted as a self-evident or proverbial truth.
The appeal of paradox lies in the fact that, however contradictory it may seem to be to the accepted maxim, it contains nevertheless, a certain grain of truth, which makes it an excellent vehicle of satire...
AND, to your point:
Wilde’s epigrams and paradoxes have another important function also. It is the showing of bourgeois morality. With the help of his epigrams and paradoxes the author shows us his characters, their way of life, manners, their thoughts and the bourgeois society of his time.