Just like the name said, asymmetrical hairstyle means that you will have your hair cut asymmetrically and not even in both sides. Mostly, the bangs will be cut straight across and even, but the rest of your hair is not. You have to know that there are a lot of asymmetrical variations that can be done into your hair. Your bangs may look straight but its angle can be done in any shape. Here are some references that could suits your face so you will have greater looks than before.
Wavy Casual Asymmetrical
This type of cut will let your side and back hair cut, with an addition that one side is pulled behind one ear. It will leave the opposite side out and show off the textured curls and braids. Your top hair will be smoothed over to one of the sides, letting your face covered a little bit and soften the overall look. When it comes to styling, this type of hair needs extra hold and shine. You need time to make the braids stand out.
Straight Alternative Pixie
This type of cut will have its shorthair side and back tapered into the head, blending to the top of the hair. Then, it will swept to either sides for shaping and styling. To soften the face and complete the overall looks, the front part of the hair will flipped over the forehead. You have to trim the hair once every four to six weeks. It also needs additional treatment to hold the style in place.
This hair cut will needs the side and back of your hair to be short, complimented with one of the side pulled behind one ear and leave the opposite side out and shown the textured cut ends. To soften the overall look, the front part of the hair needs to fall to the face by smoothing it over to one side. This is a versatile asymmetric cut that needs product for shine and hold.
This haircut will let your hair to be graduated up the back for easier shaping. It is complemented with angled layers through the sides and front blending in. This will create the asymmetric look but it also looks formal. Mostly, curls will be added to fill the empty zones and give this the hair brilliant boosts.
That is some types of asymmetrical hair as your reference. Of course those are not the only types of asymmetrical. You should find asymmetrical hairstyle that suits your face the most.