Strength (STR): Determines your probability of hitting an enemy (along with Dexterity and your level)

Determines how much damage you do in short-ranged combat

Determines, along with your seven souls gold Constitution, your carrying capacity

Strength helps in determining your probability of hitting an enemy (with a melee weapon).

"It [probability of landing a hit] is also based upon weapon enchantment (a +6 weapon has a +3 to hit), and weapon hit bonuses, and your Strength." -- Melantus 4/25/02

We do not know how much the Str spell helps in hitting monsters, but it does in fact increase the probability.

Strength helps determine how much damage you do in short-ranged (melee) combat.

Strength only helps in melee combat and not in ranged attacks (bows). The greater your strength, the harder you will hit an enemy and thus the more damage you will inflict.

The following chart from Lineage Compendium shows the effect of Str to be as follows: 

All of these will help in giving you your lawful points. South of the Kent Bridge you will find Dwarves, Dwarf Warriors, and Werewolves. These are good monsters to kill but are also a bit difficult. Not to mention, the dwarves do not give any lawful points.