What are the best ways of reducing significantly high triglyceride levels  when statins are not helping?

Lifestyle/meds. Weight loss through diet and exercise can have a very beneficial effect on triglycerides. If diabetic or hypothyroid, control over these helps. Omega3 fatty acids help but can raise LDL (fish oil 2 grams twice daily, 1/4 cup walnuts/day, use of olive oil for dietary oil such as on spinach salad). Fibrates (prescription) are very effective.
Lower carbs. Some patients have genetic predisposition to elevated triglycerides, but for most folks, going on a lower carbohydrate diet can help decrease triglyceride levels. Carbohydrates/starches are a staple of western diets. Foods high in carbs include pizza, pasta, rice, potatoes, beer, breads and cereals, mexican food. Ask your physician to guide you if you have any questions.
Wt loss + low carbs. Statins don't usually help triglycerides. Weight loss, avoiding alcohol, and a low carb diet usually help. High doses of fish oils or Niacin can help if the above measures don't.
Carnitine. For high triglycerides you need both carnitine and b2 in high doses atleast 2gm carnitine per day and redraw levels in 30 days if no response then ask your doctor to prescribe Lovaza -.
Omega 3. Statins are not generally the mainstay for treating elevated triglycerides. High quality omega 3 are the first choice but if levels are significantly elevated (putting you at risk of pancreatitis), Niacin and fibrates are considered better choices.