The season goes from April to November. In that time air from spring 10-20°C, in summer up to 30°C and autumn 10-16°C. Water spring 8-13°C, summer 18-23°C, autumn 8-14°C. You always need a wetsuit. You can go out off-season but it will be very cold, a thick wetsuit or better drysuit, mask, shoes and gloves recommended.
Take E45 to Kolding, take exit no.64 onto E20 towards Esbjerg. Take exit no.75 onto 463 until Billum, left in the round about, take 431 to Oksbøl. Keep driving through Vejers until you reach Vejers Strand. You can park directly on the sandy beach.