When tasked with creating a widget in OmniStudio that aggregates and calculates information from multiple unrelated objects, the most appropriate tool to accomplish this declaratively is Integration Procedures (Option A). Integration Procedures in OmniStudio are designed to handle complex data operations that involve multiple objects, potentially including data aggregation, transformation, and logic application, without requiring custom code.

Option B, MuleSoft Integration, is primarily used for connecting Salesforce with external systems, not for aggregating data within Salesforce.

Option C, SOQL Queries, can retrieve data but do not themselves handle complex multi-object calculations and logic in a declarative manner.

Option D, Apex Classes, are a coding solution, not declarative, and would be used when more complex custom behavior that cannot be achieved declaratively is required.

Integration Procedures allow a declarative approach, fitting the need to work with multiple objects effectively and efficiently within the Salesforce platform.