We present ORQ, a system that enables collaborative analysis of large private datasets using cryptographically secure multi-party computation (MPC). ORQ protects data against semi-honest or malicious parties and can efficiently evaluate relational queries with multi-way joins and aggregations that have been considered notoriously expensive under MPC. To do so, ORQ eliminates the quadratic cost of secure joins by leveraging the fact that, in practice, the structure of many real queries allows us to join records and apply the aggregations "on the fly" while keeping the result size bounded. On the system side, ORQ contributes generic oblivious operators, a data-parallel vectorized query engine, a communication layer that amortizes MPC network costs, and a dataflow API for expressing relational analytics -- all built from the ground up. We evaluate ORQ in LAN and WAN deployments on a diverse set of workloads, including complex queries with multiple joins and custom aggregations. When compared to state-of-the-art solutions, ORQ significantly reduces MPC execution times and can process one order of magnitude larger datasets. For our most challenging workload, the full TPC-H benchmark, we report results entirely under MPC with Scale Factor 10 -- a scale that had previously been achieved only with information leakage or the use of trusted third parties.