How many months does allergy shots (dust, pollen, grass, weed) generally take to take effect on average? 3 or 6 or 12 months? (Approximately)

By 12 months. Depending on the schedule but nearly all should have responded by 12 months (some as early as 3 months). If you still have had no response, then you will need to review your environmental control measures (dust mite, pet , mold etc) . If these have been completed and you have derived no benefit by 12 months, the situation needs to be reassessed.