Using a sharp knife, trim and halve oranges. Remove the pithy core of the oranges, discarding any seeds. Cut the orange halves into thin slices (with peel); halve slices. In a large bowl, soak oranges and any juices in 3 cups of water for 8 hours.
Wash strawberries, remove the stems and cut strawberries in half. Strip thyme leaves off of stems and combine with strawberries. Place in large pot; cover with sugar and let sit for one hour.
Remove the soaked orange slices from the water (reserve water incase jam needs to be thinned out at the end, discard water once jam is done), salt and pepper and add to the pot with the strawberry mixture.
Cook everything on low-medium heat, stirring regularly and gently mashing fruits as you go, until it is reduced by more than half and reaches 220 degrees.
To check if the jam is ready; freeze a spoon in the freezer. Pour a few drops of hot jam on the frozen spoon. Wait a couple seconds to see the consistency of the jam or swipe your finger through the jam to check for thickness. Cook a little longer if the jam is still too saucy.
Place jars and lids in large pot with hot water (not boiling). Leave them covered in about about 2 inches of water until ready to use.
Ladle hot sauce into jars, leaving ¼ inch of space on top and close with lid. Put upside down for couple of hours.
When the jam is cooled off, you can store it in the fridge for up to three weeks.