A creature can score a critical hit with an attack that deals ability damage. The Monster Manual on Ability Score Loss, in part, says
If an attack that causes ability damage scores a critical hit, it deals twice the indicated amount of damage (if the damage is expressed as a die range, roll two dice). (305)
Further, if the DM rules that the feat Improved Natural Attack (MM 304) can be applied to a creature's incorporeal touch attack, the feat may increase the shadow's 1 point of Strength damage to 1d2 points of Strength damage (Dungeon Master's Guide 28). If it does, that means the shadow qualifies for the feat Empowered Ability Damage (Libris Mortis 26) so as to increase that damage to a whopping 1d2+1.
Presumably, changing size also increases that ability damage, but the typical way for a low-level creature to do that—the 1st-level Sor/Wiz spell enlarge person [trans] (Player's Handbook 226–7)—is closed to a shadow because of its undead type. Instead, rely on the 1st-level psion/wilder power expansion [psychometabiloism] (Expanded Psionics Handbook 105–6) that works no matter a creature's type.
However, a shadow PC will survive events that will kill the rest of a normal adventuring party. At low levels, a shadow's big worry shouldn't be surviving battles against pedestrian foes—normal foes of low-level PCs like goblins and kobolds will have no way to affect an incorporeal creature—, and a shadow shouldn't worry about contributing—if the 1 point of Strength damage leaves the creature unphased, the feat Ghostly Grasp (LM 27) lets a shadow use a normal morningstar, proficiency with it and all simple weapons granted by the type undead (MM 317).
Instead, a low-level shadow PC should worry about clerics and their ability to turn and rebuke undead. The former can destroy a shadow, and the latter enslave it—and both pretty much end that shadow's (second) story. Thus, instead of feats that increase a low-level shadow's Strength damage, I recommend feats that grant it turn resistance like Improved Turn Resistance (LM 27—8) and Lifebond (28). (While a PC shadow gets +2 turn resistance at level 7, that's way too late.)