According to wiki information (from UESP and Wikia), you get experience in skill based on base damage and not the number of hits or the damage done. As such, damage multipliers do not provide any extra experience to skill.
You can try finding a trainer or use following books to get some skill points:
The following books also increase the player's skill, with some easier ways to get them:
- 2920, Morning Star, v1 (In Northwatch Keep - On a shelf behind the counter in the dining area.)
- Fire and Darkness (No real easy way to get it)
- Mace Etiquette (In Fort Greenwell's Captain's Quarters, on the floor.)
- Night Falls on Sentinel (Can show up as random loot in chests.)
- The Importance of Where (In Jorgen and Lami's House in Morthal - inside the bucket on the barrel to the left of the bed.)
- Oghma Infinium (Gained through a quest "Discerning the Transmundane" and disappears after reading.)
The following miscellaneous quests increase the One-Handed Skill:
- Retrieve Amren's family sword for Amren in Whiterun. This also
- Retrieve Hjalti's sword for The Ghost of Old Hroldan at Old Hroldan
Inn. This also increases Block.
- Find Rjorn's Drum for Giraud Gemane in The Bard College in Solitude.
This also increases all other combat-oriented skills such as Heavy
Armor and Smithing.
- Help Wulf Wild-Blood in Skaal Village find out what became of his
brother. This also increases Block, Archery and Heavy Armor. (Dragonborn DLC only)
Following people can help you train your skills for money:
- Amren of Whiterun (Common)
- Athis of the Companions in Whiterun (Expert)
- Chief Burguk in Dushnikh Yal (Master)
If you want to use less legitimate ways, certain targets can serve as an exploit for training combat skills, because they are essential, and therefore cannot normally die, because they may be expendable, or because they have high health or can regenerate health. They are not normally "enemies".
They include: Shadowmere, Hadvar or Ralof during Unbound, creatures you have conjured, Paarthurnax (before starting his quest), and M'aiq the Liar.
Another, more "easy" way is to use trainers then pickpocket the money back. Becoming Harbinger of The Companions will also allow training to expert level with Athis and you can have him as a follower which allows all the gold spent training to be returned (take it from his inventory).