Learn Croatian: Mi volimo sok i sir. - We love juice and cheese.

The dictionary form is voljeti (to love). Like many verbs ending in -jeti, you drop the -jeti to get the stem (vol-) and add the present tense endings. For 'we', the ending is -imo, making it volimo.

Is the word mi (we) strictly necessary in this sentence?

No, it is optional. Because the ending -imo in volimo already tells us the subject is 'we', you can simply say Volimo sok i sir. Including mi just adds a bit of emphasis, as if saying 'We are the ones who love juice and cheese.'

Since juice and cheese are the things being loved, shouldn't their endings change for the accusative case?

They are actually in the accusative case here! Both sok and sir are masculine nouns. In Croatian, when a masculine noun is an inanimate object (a thing, not a living being), its accusative form stays exactly the same as its dictionary form.