Oilcloth is a PVC product so you never want to take an iron to it. Instead we have to get tricky when sewing seams that we would normally press. I have 3 simple methods for you to try; finger pressing, book pressing and crease pressing.
Book Pressing is very easy, but it can cost you time. It's best for projects that need a really crisp edge or for really thick seams. Simply lay a stack of books on top of your seam(s) for a few hours or overnight. Gravity and the weight of the books flatten out your oilcloth so you can stitch with ease.
This next one is just a good old finger press. All you do is rub your finger, thumb or the palm across the seam that you need to be flatten and tamed. Tip: I always press both my seams off to one side when working with oilcloth, it's just gives you a nicer finish. Trust me trying to keep open seams flat on oilcloth is a losing battle.
The last method I have for you is the crease press. I do this when I work with the 1" oilcloth trim that I used on the floor mat in At Home with Modern June. All you have to do is fold your trim in half and rub the oilcloth trim along the edge of your table. This just creates enough of a crease down the center so you can sew fast and free!
I hope this helps you in your addiction to oilcloth!