Strength of the heart would be emotional strength. Katniss builds a wall around herself so she won’t have to face her emotions. For her, strength is actually giving in to her feelings. She decides to trust Rue.
My wounds recovering, my mind still a bit foggy from the venom, and the warmth of Rue at my side … have given me a sense of security. (p. 209)
Emotional strength can also mean doing what’s right. For example, when Rue dies, Katniss does not just go on playing. She pauses briefly to honor her.
Strength of mind means being able to use your head in moments of crisis. Katniss is able to do this at several times before and during the games. Yet her biggest stroke of genius comes when she finds a way to ensure both she and Peeta win the games.
Maybe they don't care if we both die. ... I lift my hand to my mouth taking one last look at the world. The berries have just passed my lips when the trumpets begin to blare. (p. 345)
Katniss does not realize that she sparks a revolution with this simple but brilliant act, so bravely defying the Capitol.
Finally, Katniss does also have physical strength. She relies on her agility and speed as a hunter, which is sometimes better than being able to lift a lot of weight.
Haymitch has never seen me run. Maybe if he had he’d tell me to go for it. Get the weapon. Since that’s the very weapon that might be my salvation. And I only see one bow in that while pile. (p. 149)
Katniss uses her emotional strength, mental strength, and physical strength to survive and keep Peeta alive to the end of her first Hunger Games.