Studies on the effects of air pollution and more generally environmental exposures on health require measurements of pollutants, which are affected by measurement error. This is a cause of bias in the estimation of parameters relevant to the study and can lead to inaccurate conclusions when evaluating associations among pollutants, disease risk and biomarkers. Although the presence of measurement error in such studies has been recognized as a potential problem, it is rarely considered in applications and practical solutions are still lacking. In this work, we formulate Bayesian measurement error models and apply them to study the link between air pollution and omic signals. The data we use stem from the "Oxford Street II Study", a randomized crossover trial in which 60 volunteers walked for two hours in a traffic-free area (Hyde Park) and in a busy shopping street (Oxford Street) of London. Metabolomic measurements were made in each individual as well as air pollution measurements, in order to investigate the association between short-term exposure to traffic related air pollution and perturbation of metabolic pathways. We implemented error-corrected models in a classical framework and used the flexibility of Bayesian hierarchical models to account for dependencies among omic signals, as well as among different pollutants. Models were implemented using traditional Markov Chain Monte Carlo (MCMC) simulative methods as well as integrated Laplace approximation. The inclusion of a classical measurement error term resulted in variable estimates of the association between omic signals and traffic related air pollution measurements, where the direction of the bias was not predictable a priori. The models were successful in including and accounting for different correlation structures, both among omic signals and among different pollutant exposures. In general, more associations were identified when the correlation among omics and among pollutants were modeled, and their number increased when a measurement error term was additionally included in the multivariate models (particularly for the associations between metabolomics and NO2).