Is it possible to summon creatures without the sword of summoning

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.

I suggest using only major healing potions for the first round, while directing yourself to the parts where the demon clusters are the thinnest. Use a major healing potion as soon as the cooldown is over, especially at the wall. What you want to aim for are single demons. Don't be afraid to hit those, since you have more than enough HP to survive.

Once you get teleported back, go to the bottom row as soon as possible and summon an imp. It will kill the ghosts as well as eat through a wall. On your final teleport back, go to the bottom row again (avoid fireballs whenever necessary) and summon another imp, which will cut through the hoard of ghosts to the demon. Use invincibility and spam fire scrolls, and you should be done.