A common approach to protecting data confidentiality again-st potential adversaries is to encrypt the databases. Nevertheless, it is infeasible to perform meaningful computations on a ciphertext. Trusted Execution Environments (TEEs) offer a promising alternative by enabling computations on plaintext within a secure enclave, thereby supporting rich and complex queries. However, existing works either fall short in providing strong oblivious guarantees, fail to support queries such as non-equi joins, or suffer from significant efficiency bottlenecks. In this paper, we first address the oblivious order counting and encoding problem in a parallelized manner, enabling the counting and encoding of elements that satisfy a given order within an unordered sequence. Building on this, we propose parallelizable non-equi join algorithms for both single condition and multiple conditions. The experimental results show that our scheme completes a non-equi-join with a single condition, producing 16,000,000 output records in 26.4 s, and a multiple conditions non-equi-join producing 26,366,724 output records in 19.4 s, achieving up to 4.7 \(\times \) and 2.04 \(\times \) speedups over the state-of-the-art scheme, respectively.