In the forge, you can enchant the sword with different scrolls. What are the different enchantments I can get and what is the effect of each?
You can use a Scroll of Fire to enchant a Fire Sword, which does a small amount of additional damage.
You can use a Health Potion to enchant a Life Sword, which awards you some health back on hit.
You can use an Imp Invocation Scroll to enchant a Sword of Summoning, which has a chance when you kill an opponent to summon a friendly minion in it's place, which can act as a meat shield to protect you and kill enemies.
Which you use is primarily a matter of style. The Summoning Sword is clearly better against a number of trash mob types, but it tends to fall flat against bosses or other foes with high HP. The Life Sword offers longevity, but you lose some offensive punch, etc.
The wiki gives details on all of the swords including the different enchantments whose functions vary based on the level of the sword (SL):
Note that the swords of Life and Summoning only give you the additional benefit if you successfully kill a monster, in other words they don’t help you kill them, so you must already be strong enough to kill them to get the effect.
Once you pick one, you are stuck with it (assuming you don’t cheat), but once you beat the Developper’s Computer, you can create a level three bug to get a 33% chance of combining all three into the Sword of Liflamesummoning which as you guessed, combines the effects of all three enchantments. Its Sword of Life effect is the same, as is its Sword of Summoning effect, however its Sword of Flame effect is about 2x as much; it does 16+SL×5 damage.
(I say about 2x because the Sword of Flame doesn’t always do up to 2.5×SL because the SL÷2 part rounds down, so if the sword has an odd level, then it won’t be quite 2.5×SL, but the Sword of Liflamesummoning has no division, and thus no rounding; it always does 5×SL of damage.)
After that, there is only the Sword of Randomness which apparently is just as likely to kill you as the monsters.