If your sashiko projects are cotton just like most of mine, you can machine wash them. Use gentle setting, warm water and regular laundry detergent. If washing Indigo dyed cotton or linen, the color runs, so make sure to wash separately. However, when Indigo color runs and slightly dyes the light colored sashiko thread we consider this as a characteristic of sashiko.
Tumble dry is Ok and avoid exposure to sun if you are line drying indigo. If your projects are wool, follow the care instruction for wool fabrics. If silk is the material you used, only washable silk can be washed at home.
You can iron items with the medium hot iron setting from the back, or cover the item with a fabric if ironing from the front. Ironing will make your stitches settled.