The most important things to have for the endgame battles are Stat Raisers, Element Barriers, Life Guards, and plenty of party-wide healing items such as Hyper Blends, Jubilee Grails, Neo Tonics if you've saved them, or even Radiant Soma if you can afford it; but buy lots of the first three items I mentioned before you worry about Radiant Soma (and since you're using Ezra, who can heal, healing items are less important in general, especially if he's inherited Sybil's skills). Most of these items can be bought in the Castle in the Sky. Pepp Pep, Rory's Brew, Regina's Wine, and Unicorn Horns are essential as well (however, the Wine is less important, especially taking into account Pepp Peps, which fully restore both HP and EF).
During the first battle with Astaroth, he places a limit on your stats, rendering Stat Raisers useless, but Element Barriers and Life Guards are still important. You will definitely want to use all three for the second battle, however. Remember the healing items as well. If you don't have all this, you can lose to Astaroth and choose to return to the previous area so you can go back to the Castle in the Sky and buy the items you need (but you'll have to redo all the battles up to Astaroth when you come back to the Elemental Shrine).
As for the second battle with Astaroth... he begins in "Omni" mode, and will use Spectral Beam right away. It's probably best to Guard the first turn, then pump up with Stat Raisers/Element Barriers/Life Guards on the next turn, using your fourth character to heal the massive damage Spectral Beam undoubtedly caused (ALSO don't forget to renew the effects of these items every few turns by using them again). In Omni mode, Astaroth ABSORBS all Elemental magic (though you'll probably want to focus more on physical attacks for this battle anyway, except perhaps in Ezra's case). Here are Astaroth's other resistances and weaknesses depending on his forms:
FIRE: Absorbs Fire/Light/Sun/Star/Spirit, weak to Undead/Reptile/Humanoid-harming weapons
EARTH: Absorbs Earth/Iron/Gold/Body/Space, weak to Beast/Machine-harming weapons
AIR: Absorbs Air/Thunder/Wood/Mind/Time, weak to Plant/Insect/Avian-harming weapons
WATER: Absorbs Water/Ice/Darkness/Moon/Heart, weak to Morph/Demon/Aquan-harming weapons
And now, for each enemy type's weaknesses:
MORPH: Knuckles/Claws
UNDEAD: Katars/Knives
PLANT: Axes/Fangs
REPTILE: Swords/Katana
AVIAN: Bows/Crossbows
AQUAN: Polearms
HUMANOID: Balls/Guns
BEAST: Flails/Whips
DEMON: Hammers/Staves/Rods/Maces
INSECT: Discs/Boomerangs/Pinwheels/Chakram
MACHINE: ??? (a select few weapons of no particular type)
Also, DON'T FORGET to read the descriptions of the weapons you're using. Even if you're using a certain sword, for instance, it may have the special quality of being effective on Demons, regardless of its weapon type.
If you want, I can give you recommendations for equipment. Let me know what weapons, accessories, etc. you're using for your characters, and I'll see if there isn't something better for you to find (if you haven't found it already). Also, has Ezra inherited Sybil's healing skills in your game? If not, you may want lots of healing items after all.