It probably didn't get answered the first time because what Dennison says is literally all we know. It's almost a word-for-word transcription of what Suetonius says about Augustus' villa at Capreae. To my knowledge this is the only reference we have to Augustus'...internal decorating:

Ampla et operosa praetoria gravabatur. Et neptis quidem suae Iuliae, profuse ab ea exstructa, etiam diruit ad solum, sua vero quamvis modica non tam statuarum tabularumque pictarum ornatu quam xystis et nemoribus excoluit rebusque vetustate ac raritate notabilibus, qualia sunt Capreis immanium beluarum ferarumque membra praegrandia, quae dicuntur gigantum ossa, et arma heroum.

He disliked large and elaborate palaces. Indeed, he even razed to the ground one his own granddaughter Julia had built at great expense. His own villas, which were as modest as you like, he decorated not so much with decoration of statues and pictures as with colonnades and groves and objects notable in their antiquity and rarity, of which sort were the colossal bones [literally "limbs," but "membra" can mean as a sort of transferred epithet "bones"] of huge sea monsters and wild beasts at Capreae, which are called the bones of giants, and the arms of heroes

That's literally it, that's all we know. There's really nothing more we can say, it's as much a mystery to classicists as to you and the original poster what these were. We know that heroic relics were common in antiquity--Alexander, for example, saw the supposed panoplies of several heroes who fought at Troy when he visited the city and received a shield and armor claimed to have been used in the Trojan War, which he had carried before him before battle. Undoubtedly Augustus' relics were of the same nature