To test an ActivePivot-based project, the simpler is to re-use your Spring configuration. This can be done with ClassPathXmlApplicationContext:
ApplicationContext context = new ClassPathXmlApplicationContext("beans.xml");
This simple test will check if your Spring is actually Ok. Then, if you want to run a query, you could do the following:
IQueriesService queriesService = context.getBean(IQueriesService.class);
queriesService.execute(new MDXQuery(someMDX));
If you want to check your loading layer, you can do:
IStoreUniverse storeUniverse = context.getBean(IStoreUniverse.class);
for (IRelationalStore store : storeUniverse.values) {
assertEquals(hardcodedValue1, store.getSize())
assertEquals(hardcodedValue2, store.search("someKey", "someValue").size())
}
This way, you don't need to start a web-app container, which may fail because it needs some port to be available (meaning for instance you can't run several tests at the same time).
Post-Processors should be either Basic or DynamicAggregation post-processors, which are easy to test: focus on .init and the evaluation methods called on point ILocations. Advanced Post-processors can not be reasonnably unit-tested. Then, I advice writing MDX queries as simple as possible but relevant given the Post-Processor.
Any unit-test framework and mock framework could be used. Still, I advice using JUnit and Mockito.