I want to know who was the asura Bala, and the reason why he was killed by an avatar of Vishnu
Bala and Mahābala are two of the thirteen Saiṃhikeyas mentioned in the the Śivapurāṇa. The Saiṃhikeyas are the sons of the Asura Simhikā (source). They were vanquished by Bhārgava, also known as Paraśurāma (son of Jamadagni), which is considered to be an avatar of Viṣṇu.
The names Bala and Mahābala are mentioned Purāṇas, for example, Śivapurāṇa V.32.34-36:
34) Due to the intermixture of Daityas and Dānavas these sons became valorous and famous as Saiṃhikeyas. They are thirteen in number.
35-36) They were the very powerful Rāhu and Śalya, Bala, Mahābala, Vātāpi, Namuci, Ilvala, Svasṛpa, Ajika, Naraka, Kālanābha, Śaramāṇa and Śarakalpa. These increased their races.
While the Brahmāṇḍa-purāṇa III.6.18-22 mentions their demise:
22) The groups of Saiṃhikeyas are remembered as consisting of ten thousands. They were killed by the powerful Bhārgava (Paraśurāma) son of Jamadagni.
However, altough this Purāṇa also mentions thirteen names of which some are similar to the Śivapurāṇa, the names Bala and Mahābala are not mentioned.