Did the following test: equipped northern cross VII twohanded, with 50 mag and 30 str, and cast a Lightning storm for 73 damage. I then equipped blacksmith gloves and damage changed to 75. I removed gloves and ring to lower str to 27 and damage of lightning storm went down to 71. I tried then with northern cross one handed with cocoon battledore offhand, damage of spell lightning storm went up to 93. I repeated same test with black widow alone and damage was 65. With black widow and wand, damage was again 93. I tried with buff arcane weapon with both northern cross alone, then black widow, then dualwielding with wand, and the damage stayed the same. Lastly I equipped warhammer, which was having an higher physical attack but not total attack compared to northern cross, and damage of lightning storm was higher at 85.
My conclusion is: damage of incantations are affected by PHYSICAL total attack of weapon equipped, but offhand weapon is prioritized. The elemental damage portion of the weapon like arcane, fire, poison, lightning and holy is not taken in account in this calculation, but only the physical attack scaled by STR and MAG (I presume with WIS and DEX also?). Weapon buffs does not affect this calculation, but stat increasing equipment is effective. Note that staves and wands attack is physical damage, not elemental, so a spellcaster with only MAG can cast effective incantations. Maybe the only buff that would affect this would be goldenwine?
Lastly all these tests found out that with Prayers nothing affect its damage, only WIS.