Strength-

Strength affects three major things, for every point of strength you have, you are able to carry 10 more lbs. Secondly, for every strength bonus, your damage changes by 1 point. Mordors "rolls the dice" of the weapon you are using to determine the base damage you do when you attack, then adjusts that number according to your strength. Thirdly, your strength affects your THAC0 which stands for To Hit Armor Class 0. It's usually a number from 1-20. When you try to hit something, the game "rolls" a 20 sided die to figure out if you hit.

Dexterity-

First, the better your dexterity, the better you hide, flee and the better you can avoid traps. Secondly, your dexterity has a rather large effect on your AC. For every dexterity bonus you have, your AC is adjusted by 5. This might seem like an awful lot to you, but mordor Muds go between -60 to 110. 

Constitution-

First, when you are poisoned, the higher your con, the less hp you lose each time the poison takes effect. Secondly, the higher your con bonus, the more hp you tick for. Also, every time you log on, a hidden statistic, Luck, is determined for your character. Luck affects nearly everything you do to a small degree, and con affects your luck.

Intelligence-

First, it affects whether or not your spell will succeed. Intelligence also plays a large part in determining how effective and how long lasting your spells are. Thirdly, your intelligence bonus affects how quickly your magical realms go up. Yet another affect intelligence has is how well you can cast healing spells.

Piety-

First, the effect everybody knows about - your piety bonus determines how fast you tick. Secondly, piety affects your healing spells in the exact same way as intelligence - for every piety bonus, the amount you heal is changed by 1.Now for the most surprising effect piety has - it is factor in how well you search. The higher your piety, the better you search.