His strength is his shrewdness. He can make apt political decision. He is good in his ability to work with Antony. He is very decisive in his ability to step up to the plate, to meet with Brutus and Cassius. His confidence in defeating the enemies at Philippi and bringing about a new Roman empre is another strength. However, his weaknesses are his runination.
Octavius' weaknesses are: his rashness in executing a murderous reign of terror that resulted in slaughtering his enemies. However, he got rid of those who were not actual enemies. He killed wealthy Romans, saying that they were "traitors" so the triumvirs could pilfer their estates to get money for the army,which was a bad move and a weakness that would come back to haunt him in the future.
In Act IV Octavius demonstrates judiciousness. As Antony dismisses Lepidus as "a slight unmeritable man" not worth to share their power, Octabius defends Lepidus, questioning Antony:
You may do your will;/But he's [Lepidus] a tried and valiant soldier. (Iv,i,28-29)
Likewise, in his judgments that are superior to Antony's, Octavius argues against another limited assessment of Antony: his concept of the battle. In Act V, he tells Antony,
Now, Antony, our hopes are answered;/You said the enemy would not come down,/But keep the hills and upper regions./It proves not so; their battles are at hand;/They mean to warn us at Philippi here,/Answering before we do demand of them. (V,i,1-6)
Antony counters that the army of Brutus wants to make a show of braver to convince them. But, Octavius is not a man of words, but of action. He calls the bluff of Brutus and Cassius saying,
Defiance, traitors, hurl we in your teeth./If you dare fight today, come to the field;/If not, when you have stomachs. (V,i,64-66)
Yet, Octavius is not without respect. For, when Brutus dies, it is Octavius who summons the armies from the field, directing that the day's "glories" be shared:
According to his virtue, let us use him/With all respect and rites of burial./Within my tent his bones tonight shall lie,/Most like a soldier ordered honorably./So call the field to rest, and let's away/To part the glories of this happy day. (V,v,76-81).
While Octavius recognizes honor in other men, he is like his relative, Caesar and does love power. He follows the example of his adopted father and emerges as an authoritative figure of Rome.