what are willy lomans strengths? how can they also be his weaknesses?

Willy's strengths were the ability to deceive others into believing he was something he wasn't and to advance himself because of their misguided opinions and perceptions. These two things can also be perceived as weaknesses because they kept him from choosing a profession in which he'd not only excel in, but be interested in as well.

Willy Loman lived in a fantasy world.

In his mind he was capable of greatness, and that the greatness stemmed from his charisma, and his popularity.

In reality he had made a few serious mistakes, and instead of financially moving forward, he was continually losing ground.

He was indeed a fake.

He taught his sons to lie to their women, and they also mistreated them.

He did not think that stealing was wrong, or a sin, and when one of his sons told him he had stolen a football from a coach, Willy (dad) told his son that popularity and charisma will outdo hard work.

Willy was unhappy with life, I think he loathed himself because deep inside he knew he was a failure...His strength ?: He had ideals, "Be charismatic, and popular and you'll achieve greatness", and he lived by them

His weakness: His ideals, they were the WRONG ideals, they became his doom.