I think lajatang's sticking so much is an oversight. Lajatang's don't have any attack flags; thus they are treated as improvised weaponry, doubling their "stickiness".
Stickiness is dependent on the weapon's movement cost (Which is linked to their weight). Hence, heavier weapons are more prone to sticking. From what you've experienced, Crude swords are twice as heavy as 2-by-swords (both lack weapon flags), so suffer twice as much. And lajatangs weigh more than twice what crude swords do so...
Knife spears have the "Spear" tag, which halves their stickiness, which was why you had little issue pulling those out.
Higher cutting skill reduces a cutting weapon's stickiness while piercing skill does the same for piercing weapons. From what I can tell, each level is a d20, so your 3 cutting skill reduces the stickiness from anything between 3 and 60.
Moving beyond flags, having bashing damage on a weapon significantly reduces stickiness. Hence your 2-by-sword, dealing practically no cutting damage, never really got stuck. Whereas lajatangs (2 bash and 26 cutting), suffers from extreme stickiness.
If you want to fix this, add the weapon tags to the affected weapons. "CHOP" for crude swords and lajatangs.
Knife Spear: 113 MoveCost, 16/18 Piercing/Total damage, Spear flag (50%),
113 X 0.89 X 0.50 = 50.285 Stickiness
2-by-sword: 95 MoveCost, 1/13 Cutting/Total damage, No Flag (200%)
95 X 0.08 X 2 = 15.2 stickiness
Crude Sword: 115 MoveCost, 14/20 Cutting/Total damage, No Flag (200%)
115 X 0.7 X 2 = 161 stickiness
Lajatang: 210 MoveCost, 26/30 Cutting/Total damage, No Flag (200%)
210 X 0.87 X 2 = 364 Stickiness
Yanking your weapon free is a strength check with (STRx2)d20, with 11 str you roll between 22 and 440. Since a lajatang has 364 stickiness, you'll fail about 80% of the time. There's still other checks though.
With proper tags:
Crude Sword: 115 MoveCost, 14/20 Cutting/Total damage, "CHOP" Flag (100%)
115 X 0.7 X 1 = 80.5 stickiness
Lajatang: 210 MoveCost, 26/30 Cutting/Total damage, "CHOP" Flag (100%)
210 X 0.87 X 1 = 182.7 Stickiness