We investigate the six most massive Illustris galaxy clusters in the Illustris simulation (Nelson et al. 2015) at z=0.2 and z=0.44 in terms of their dynamical state and their strong gravitational lensing properties. For this, we present illcrawl, a new software for the efficient reconstruction and visualization of Illustris data with GPUs. illcrawl is used to apply to our clusters the method by Mantz et al. (2014), which estimates the dynamical state of galaxy clusters based on their X-ray morphology. We find that this method considers those clusters as relaxed that appear undisturbed in terms of their X-ray gas, indicating that this method works as expected with simulated galaxy clusters. The clusters that are considered un- relaxed feature prominent “bubbles” in the X-ray gas due to the Illustris AGN feedback model. The virial ratios for all clusters hint however at mostly relaxed systems. We also show how regions can be determined where strong gravitational lensing effects are expected. We find that strong lensing in Illustris clusters is expected mostly on scales of individual galaxies. All our detected lensing regions are observable, i.e. we find no “dark lenses”. All our strong lensing regions show a tight correlation between stellar content and total mass.