Strength/Experience rewards

You can get Strength experience as rewards for completing certain quests:
 * 100 - The Blood Pact
 * 600 - In Search of the Myreque
 * 2,000 - In Aid of the Myreque
 * 2,500 - Tai Bwo Wannai Trio
 * 2,812 - The Fremennik Trials
 * 3,000 - Land of the Goblins
 * 3,075 - Heroes Quest
 * 4,000 - Troll Romance
 * 4,662.5 - Horror from the Deep
 * 5,000 - TokTz-Ket-Dill
 * 6,625 - Scorpion Catcher
 * 9,000 - The Curse Of Arrav
 * 10,000 - The Fremennik Isles (can be doubled)
 * 10,000 - Roving Elves
 * 13,750 - Waterfall Quest
 * 18,650 - Dragon Slayer
 * 20,000 - Fremennik isles
 * 20,000 - The Chosen Commander
 * 20,000 - Monkey Madness (optional when you speak to Daero, you can get 35,000 instead of 20,000 if you choose Attack and Strength over Defence and Constitution)
 * 22,000 - Haunted Mine
 * 30,000 - The Path of Glouphrie
 * 30,000 - Forgiveness of a Chaos Dwarf
 * 55,000 - King of the Dwarves

Total: 294,774.5 Experience

There are lots of quests and tasks that allows the player to choose the skill that will receive an experience reward. These are the choice rewards that can be spent on Strength, altho it is reccomended to use them on skills that are harder to train.
 * A Fairy Tale Part II - A skill lamp granting 2,500 exp in any skill.
 * A Tail of Two Cats - Two antique lamps granting 2,500 exp in any skill above level 30.
 * Blood Runs Deep - 3 training sessions that grant 150,000 exp in any combat skill (except summoning) above level 75.
 * Contact! - Two 'wishes' each granting 7,000 exp in either Strength, Summoning (if higher than level 30), Attack, Defence, Magic, Ranged, or Constitution.
 * Darkness of Hallowvale- A tome of experience with three chapters giving 2,000 experience in any skill above 30.
 * Dream Mentor - Dreamy lamp which gives 15,000 experience in any combat skill except from Attack or Prayer.
 * The Fremennik Isles - Two lots of 10,000 each that ban be spent on in Attack, Strength, Defence or Constitution.
 * Glorious Memories - A lamp granting 2,500 exp in any skill (received as an additional reward after the quest) and a tome with 3 chapters, granting 5,000 exp per chapter in one of the following skills: Attack, Strength, Defence, Constitution, or Ranged.
 * The Great Brain Robbery - Blessed lamp granting 5,000 exp in any skill above 30.
 * King's Ransom - A skill lamp granting 5,000 exp in any skill above level 50.
 * Legacy of Seergaze - A tome of experience with three chapters, giving 2,500 xp each in any skill above 35.
 * Legends Quest - 7,650 exp in any four of the following skills: Attack, Defence, Strength, Constitution, Prayer, Magic, Woodcutting, Crafting, Smithing, Herblore, Agility, Thieving.
 * Love Story - After returning Mabel's ring to Mabel you receive a lamp granting 10,000 exp to any skill over level 60.
 * Meeting History - A skill book with 3 chapters, 2 chapters giving 1,000 exp and 1 with 500 exp in any skill above level 25.
 * Monkey Madness - 35,000 experience in Attack and Defence or Strength and Constitution, and 20,000 experience in the other two skills. Talk to Daero after the quest to receive these rewards.
 * Myths of the White Lands - Provides a 500 exp lamp that can be used in any skill.
 * One Small Favour - Two reward lamps each granting 10,000exp in any skill above level 30.
 * Recipe for Disaster - A lamp granting 20,000 exp in any skill above level 50.
 * Shadow of the Storm - 10,000 exp in any combat skill except Prayer and Summoning.
 * The Tale of the Muspah - After completion, the player can talk to the Natural Historian for a lamp worth 200 exp in any skill.
 * Troll Stronghold - Two skill lamps each giving 10,000 in a skill above level 30.
 * Tutorial island or Learning the Ropes - Two experience lamps granting 250 exp in any free skill, other than Crafting, Runecrafting, or Dungeoneering.
 * While Guthix Sleeps - After talking with Idria you receive 4 lamps that grant 100,000 exp in any skill above level 65.