Use a good quality thread to minimise the danger of snapping
You may find that the oilcloth feeds better when sewing if you use a special feeder foot on your sewing machine. This will lead to more even stitching.
In general, the thicker the fabric the longer the stitches you should use. If sewing more than one thickness of oilcloth you may want to increase your stitch length.
Practice on a small remnant first!
If you are having difficulty attaching binding - a good trick is to stick the binding where you want it using a fabric or pva glue and paper clips to keep it in position until dry. When you come to sew you'll find it much easier.
If you find it difficult to get your binding to follow the curves of your pattern - make small incisions on the reverse of the binding which will allow it to curve more easily
Other Ideas
Add eyelets for decoration or clever fastening solutions
Sew individual sequins onto your finished item
Velcro is a quick and easy solution for creating fastening