This stitch is decorative and technically similar to the woven circle. A woven oval is done between two diagonal straight stitches. This technique of weaving ovals can be incorporated with any other stitches with straight stitches, like, between two diagonally placed cross stitches.

woven_oval_1     woven_oval_2
Fig 1: Stitch two straight stitches diagonal to each other, as illustrated.   Fig 2: Bring out the needle through the inner point of one stitch, as shown.
Take the needle beneath the other stitch, without plucking the fabric underneath.
woven_oval_3    woven_oval_4
Fig 3: Go around for the second time, under the straight stitches. Finish up by taking the needle in through the point from where it started.    Fig 4: A finished woven oval looks like this.