As you can see, my character has nothing in his inventory -

http://i.imgur.com/q7hpJrh.png

but encumberance reads 68! All my stats are normal.

Is there a mod or console command to fix this?

IIRC, you add an item that weighs 1 and then remove 69 of the same ( in console using player->additem , removeitem )

temporarily disable Morrowind Code Patch removeitem fix if you have it enabled,

then try following methods explained http://www.gamesas.com/topic/1601876-constant-effect-feather-not-working-btb-mod-guidenow-old/#entry25138442

[EDIT]also, if you post your mod list maybe we can recognize some mod(s) causing the problem