What did you use to determine up-regulated and down-regulated genes ?
I use DESeq2 and then use a p.adj cutoff of 0.05. This would be a false discovery rate of 5%. You may also want to use a log2 cutoff of greater than 1 and less then -1. It depends on how many genes you have and your own personal preferences.
On the selected genes, I use cluster3.0, http://bonsai.hgc.jp/~mdehoon/software/cluster/ , to cluster the genes and then JavaTreeView, https://sourceforge.net/projects/jtreeview/ , to visualize a heatmap of the clustered genes. You should read over the manuals for cluster3.0 and JavaTreeView. There is not much to learn, but the data needs to be in a specific format for the programs to work. If you had the data in an Excel spreadsheet, you would need to change a few column headers and make sure the gene names are in the proper column. So, there is not a whole lot of changes that need to be made, but the specific format is necessary.
For Venn diagrams, I have used BioVenn, https://www.biovenn.nl/ . Just copy and paste your gene identifiers into the proper boxes and it does a very nice job of making Venn Diagrams. The size of the circle will be proportional to the number of genes. Unfortunately, after three categories, it is next to impossible to make a venn diagram where the circles are proportionate to the number genes, so if you have more than three conditions, you will not be able to get a venn diagram where the size of the 'circle' is proportionate to the number.
Others will use R and/or python, but it depends on how comfortable you are with each.