Venn diagrams are a fun and easy way to visualise the unique and overlapping differentially expressed genes between variables in a dataset. In my experience, I find Venny to be the most useful. By copying and pasting gene lists from various comparisons, Venny allows quick identification of genes that are either shared or unique between comparisons.
Another way to draw Venn diagrams is to use the Venn diagram plotter, which allows drawing of correctly proportioned Venn diagrams. The size of the Venn diagram plotted will be proportional to the size of the gene list, allowing a visual representation of the extent of overlap between comparisons (see above for example).
Lastly, it is important to note that Venn diagrams are unable to assign gene rankings, so I would recommend doing a pathway enrichment for the different segments of the Venn diagram to prioritise the genes of interest. Alternatively, you may consider Venn-diaNet for such analysis.