Learn Russian: Какого числа вечеринка в офисе?

In Russian, when you want to ask on what date an event happens, you use the genitive case. Какое число? (nominative case) just asks what today's date is, while какого числа? literally means "of what date?" and asks when something takes place.

How is какого pronounced? I see a г but hear a "v" sound.

That is a very common spelling rule to remember! The letter г in the genitive adjective endings -ого and -его is always pronounced like an English "v". So, какого sounds like "ka-KO-va".

Where is the verb "is" in this sentence?

There isn't one! In the present tense, Russian drops the "to be" verb (is, am, are). So "What date is the party" is simply said as "Of what date the party". If it were in the past or future tense, you would need to add a verb like была (was) or будет (will be).

Why does the word for office end in -е here (в офисе)?

Офис is a masculine noun. Because it follows the preposition в to show a static location ("at" or "in" the office), it must take the prepositional case. For most masculine nouns, you form this case by simply adding an -е to the end of the word.