Although Heroes of Delphi has a historical setting, we populate the setting with the monsters of Greek myth and legend (and some others too, in the spirit of the myths). Treat these as you would the traditional Greek monsters. They aren't super abundant, they don't wander the countryside on a daily basis, they exist in out of the way places, or sent to ravage some poor city (or poor soul) by the vengeful gods.
The list that follows has been compiled from the Monster Manual, these are recommended monsters for a Heroes of Delphi campaign. Nearly all others in that book are unsuitable either on locality or flavour. New names, in keeping with the Greek setting, may be given in parenthesis.
Animals (including: Bat, Black Bea, Bison/Cattle, Boar, Cat, Dog, Donkey, Eagle, Hawk, Horse/Lt., Lion, Mule, Owl, Pony, Porpoise, Rat, Raven, Snake/Viper, Wolf)
Assassin Vine (Tantalus Vine)
Azer (Cabiri - the forgemasters of Samothrace)
Centaur
Chimera
Blink Dog (Laelaps the gifted hunting hound)
Dire Animals (various examples occur in the myths including Wolf, Bear, Boar and Lion)
Dryad
Elemental
Ettin (Orthrus)
Hill Giants (Greek giants are solitary sheep-herding barbarians, and one-eyed Hill Giants make fine Cyclopes)
Ghost
Giant Eagle (servant of Zeus)
Giant Owl (servant of Athena)
Golems (Clay, Stone and Iron - not Flesh)
Gorgon (Colchis Bull)
Griffon
Harpy
Hippogriff
Hobgoblin (Sown Man; foul warrior springing up from the sown teeth of rare dragons)
Hydra
Invisible Stalker
Lamia
Lammasu
Lillend (Echidna)
Lycanthrope
Manticore
Medusa
Merfolk (Tritons, ignore the MM 'Triton' entry)
Minotaur
Mohrg
Monstrous Spider
Monstrous Scorpion
Nightmare (Poseidon's Steed)
Nymph
Pegasus
Satyr
Shield Guardian (Talos)
Skeleton
Spectre
Sphinx
Titan (surely these are great candidates for the gods themselves! Reading the Iliad, one notices that mortal heroes can inflict wounds against the gods and sometimes defeat them in battle - just!)
Treant (Hammadryad)
Wraith
Magic Items
Just as there are many Greek-inspired monsters in D&D3E, so too there are plenty of Greek-inspired magic items. Of course the Greek myths were littered with magical devices of every kind, the god Hephaestus, for example, knocked out dozens of them! All of the different categories of magic item; armour and shields, weapons, potions, rings, rods, scrolls, staffs, wands and wondrous items all fit the setting nicely. There are no intelligent magic items, however. One thing to note about Greek magical artefacts is the fact that often they look spectacular. Often beautifully worked and ornate, made of precious metals (or at least inlaid with precious metals). There are exceptions, but generally, the magic within is mirrored by the items appearance. Obviously, with some aspects of the game traditional fantasy world absent some items cannot exist. Things like the Mithril Shirt, Elven Chain, magical nunchaku and so on. Use the notes in Heroes of Delphi as a guide. The Dungeon Master's Guide recommends that DMs provide more evocative names for magical items, and I heartily agree. Having the Greek myths as a backdrop makes such a task a breeze. A +3 Shield of Arrow Deflection? Make that the Golden Shield of Agamemmnon (who invoked the wrath of Apollo during the Trojan War and who had to watch as the god peppered his troops with deadly arrows). A Javelin of Lightning makes a wonderful Thunderbolt of Zeus (that god always had a fistful of these things!). The Robe of Eyes could be the hide of Argus (the monster with one hundred eyes). And so on. Many of the Wondrous Items resemble the exotic magical items that turn up in the myths.
Artefacts, of course, being the upper end of magical creation could potentially stand in for the relics of the Olympians, the very weapons and tools wielded by the great Greek gods in ages past. However, those listed in the DMG are not particularly suitable for a Greek campaign, but then whole purpose of artefacts is for the DM to create them especially for his campaign. In many cases high level magic items will suffice. Are Winged Boots actually the winged sandals worn by Hermes? Is a +5 Cloak of Resistance the hide of the Nemean Lion worn by Hercules?