The proliferation of association results from large-scale genetic and genomic studies provides opportunities and challenges to elucidate the disease/trait mechanisms and their operating cellular contexts. Motivated by a multi-tissue multi-omics analysis using genetics, methylome and transcriptome data from the Genotype-Tissue Expression (GTEx) project, we propose a method, X-ING (Cross-INtegrative Genomics), for cross-omics and cross-context integrative analysis of summary-level data. X-ING takes as input the statistic matrices from multiple omics studies, each with multivariate contexts. It models the latent binary association status of each statistic, and captures the omics-shared and context-shared major patterns in a hierarchical Bayesian model. Via the modeling of latent binary status, X-ING enables the cross-feature integration of effects from different effect distributions. The analysis of cis-genetic effects on methylome and transcriptome from GTEx characterizes the tissue- and omics-effect sharing patterns. The analysis of trans-genetic effects demonstrates enrichment of trans-associations in many disease/trait-relevant tissues. Many associations identified by X-ING are replicated using external data, with higher replication rates for multi-tissue or multi-omics effects.