Sending postcards and normal-sized letters (ie under 20g) by airmail is cheap but not really fast. For anything over 20g, the charge is based on weight. You can send parcels up to 20kg and have them properly wrapped and sealed at any post office (www.posindonesia.co.id).
Every substantial town has a kantor pos (post office). In tourist centres, there are also postal agencies. They are often open long hours and provide postal services. Many will also wrap and pack parcels.