Is it unusual to not ovulate with irregular periods?

Very common: If you have irregular period, most likely you have a non-ovulation cycle. Most of these bleeding are considered break through bleeding. Pcos, thyroid dysfuntion and many other conditions may cause that. I suggest you to see a gynecologist.

They're associated!: Irregular periods are caused when your body's signals for ovulation and menstruation get confused by hormonal imbalances that can be related to your thyroid (TSH), pituitary (LH/FSH/prolactin), ovaries (estrogen/progesterone). Many external factors can affect the hormones: malnutrition, stress, obesity, for example. Hormonal contraception can help to regulate your periods, which is healthier.