Learn Croatian: Ona ima nježan glas. - She has a gentle voice.

They are actually in the accusative case! In Croatian, masculine nouns for inanimate objects (like glas) and their adjectives share the same form in the accusative as they do in the nominative. If she had a gentle husband (animate), it would take the animate accusative ending: Ona ima nježnog muža.

Why is the adjective nježan used here instead of nježni?

Nježan is the indefinite form of the adjective, which we use when saying someone has "a" certain quality, like "a gentle voice." Nježni is the definite form, which translates more closely to "the gentle voice."

Is it necessary to include the pronoun ona, or can I just say Ima nježan glas?

It is perfectly fine to drop ona and just say Ima nježan glas. Because the verb ima (has) already tells us the subject is third-person singular, the pronoun is optional. Keeping ona just adds a little emphasis to who you are talking about.

Besides "voice," does the noun glas have any other common meanings?

Yes! In political or formal contexts, glas also means "vote." For instance, the phrase dati glas translates to "to cast a vote."