Process querying is used to extract information and insights from process execution data. Similarly, process constraints can be checked against input data, yielding information on which process instances violate them. Traditionally, such process mining techniques use case-centric event data as input. However, with the uptake of Object-Centric Process Mining (OCPM), existing querying and constraint checking techniques are no longer applicable. Object-Centric Event Data (OCED) removes the requirement to pick a single case notion (i.e., requiring that events belong to exactly one case) and can thus represent many real-life processes much more accurately. In this paper, we present a novel highly-expressive approach for object-centric process querying, called OCPQ. It supports a wide variety of applications, including OCED-based constraint checking and filtering. The visual representation of nested queries in OCPQ allows users to intuitively read and create queries and constraints. We implemented our approach using (1) a high-performance execution engine backend and (2) an easy-to-use editor frontend. Additionally, we evaluated our approach on a real-life dataset, showing the lack in expressiveness of prior work and runtime performance significantly better than the general querying solutions SQLite and Neo4j, as well as comparable to the performance-focused DuckDB.