Decreasing costs of modern high-throughput experiments allow for the simultaneous analysis of altered gene activity on various molecular levels. However, these multi-omics approaches lead to a large amount of data, which is hard to interpret for a non-bioinformatician. Here, we present the remotely accessible multilevel ontology analysis (RAMONA). It offers an easy-to-use interface for the simultaneous gene set analysis of combined omics datasets and is an extension of the previously introduced MONA approach. RAMONA is based on a Bayesian enrichment method for the inference of overrepresented biological processes among given gene sets. Overrepresentation is quantified by interpretable term probabilities. It is able to handle data from various molecular levels, while in parallel coping with redundancies arising from gene set overlaps and related multiple testing problems. The comprehensive output of RAMONA is easy to interpret and thus allows for functional insight into the affected biological processes. With RAMONA, we provide an efficient implementation of the Bayesian inference problem such that ontologies consisting of thousands of terms can be processed in the order of seconds.