The decentralized nature of blockchain enables data traceability, transparency, and immutability as complementary security features to the existing Internet of Things (IoT) systems. These Blockchain-based IoT (BIoT) systems aim to mitigate security risks such as malicious control, data leakage, and dishonesty often found in traditional cloud-based, vendor-specific IoT networks. As we steadily advance into the era of situation-aware IoT, the use of machine learning (ML) techniques has become essential for synthesizing situations based on sensory contexts. However, the challenge to integrate learning-based situation awareness with BIoT systems restricts the full potential of such integration. This is primarily due to the conflicts between the deterministic nature of smart contracts and the non-deterministic nature of machine learning, as well as the high costs of conducting machine learning on blockchain. To address the challenge, we propose a framework named Situ-Oracle. With the framework, a computation oracle of the blockchain ecosystem is leveraged to provide situation analysis as a service, based on Recurrent Neural Network (RNN)-based learning models tailored for the Situ model, and specifically designed smart contracts are deployed as intermediary communication channels between the IoT devices and the computation oracle. We used smart homes as a case study to demonstrate the framework design. Subsequently, system-wide evaluations were conducted over a physically constructed BIoT system. The results indicate that the proposed framework achieves better situation analysis accuracy (above 95%) and improves gas consumption as well as network throughput and latency when compared to baseline systems (on-chain learning or off-chain model verification). Overall, the paper presents a promising approach for improving situation analysis for BIoT systems, with potential applications in various domains such as smart homes, healthcare, and industrial automation.