One of the central ideas in Robert Grave's retelling of the Greek myths, published in the 1950s, is that the Greeks were influenced by hallucinogenic mushrooms in some of their rituals. This idea is probably not supported by contemporary scholarship.

He says in the introduction to the revised version of the book, published in 1955 (just called "The Greek Myths", my copy is from Penguin 2011) that "Satyrs (goat-totem tribesmen), Centaurs (horse-totem tribesmen), and their Maenad womenfolk, used these brews (ambrosia and nectar) to wash down mouthfuls of a far stronger drug: namely a raw mushroom, amanita muscaria, which induces hallucinations, senseless rioting, prophetic sight, erotic energy, and remarkable muscular strength".

He goes on at some length to cite his evidence for these claims, and also that "ambrosia" and "nectar" were "intoxicant mushrooms", fly agaric (amanita muscaria).

Aside from these types of mushrooms and wine and other alcoholic brews, I don't think there would have been any recreational drugs as we know them in the Classical world.

What was the inspiration for the lotus-eaters in the Odyssey?

I know that the Greeks did not use pot. There is a reference to it by Herodotus, when talking about the Scythians. He reported that instead of normal bathing, they would instead cleanse themselves in smoke, which would be done in a tent, with the herb burning on a holder in the middle. It did not occur to Herodotus that they would have been intoxicated from this, so it's safe to say that while the Greeks knew of cannabis, they did not know about its effects.

"The Chemical Muse: Drug Use and the Roots of Western Civilization" by Dr. David Hillman covers exactly this topic. Both the Romans and the Greeks used drugs recreationally, but they didn't discriminate between classes of drugs in the way we do. Essentially they viewed all medicines and poisons, as well as recreational substances, in the same light, differing primarily by dosage as in the principle of Paracelsus. They obviously lacked the synthetic drugs we have today, but were well aware of the effects of chemicals found in natural sources, including mushrooms, opium poppies, and marijuana. There were laws in place regarding intentional use of substances to cause harm or murder, but otherwise drugs and drug-bearing plants/fungi/etc. were treated no differently than other types of produce, much the way we treat coffee/tea/beer/tobacco/etc. People who used drugs weren't stigmatized at all, and although I'm sure people would occasionally lose themselves to the influence of intoxicating substances and be considered to have a drug problem, I don't recall any details or statistics as to how frequently that might have happened.

Yes.

Pythia Gases were used by Greek oracles.

Egyptians abused Blue Lotus. The mildly sedating effects of Nymphaea caerulea makes it a likely candidate (among several) for the lotus plant eaten by the mythical Lotophagi in Homer's Odyssey.

Opium was used by the Sumerians, Assyrians, Egyptians, Indians, Greeks, and Romans.

Psilocybin was used by ancient peoples around the Saharan desert (and North, Central and South American cultures).

Black Henbane was used by various Eurasian cultures, including the Greeks. The use of henbane by the ancient Greeks was documented by Pliny. The plant, recorded as Herba Apollinaris, was used to yield oracles by the priestesses of Apollo.

Betel Nut was used by Central and East Asian cultures. References to the Betel nut appear in ancient Greek, Sanskrit and Chinese literature as early as the first century BC.

Harmal was used by Persians. Reportedly the ancient Greeks used powdered Peganum harmala seeds.

Nutmeg has been used by Asian and Indian cultures. It was rare and expensive in ancient Roman and Greek cultures, but was available.

Grecian traders must have traded for these drugs/spices, and mobile soldiers would have certainly come into contact with them.

No one has mentioned opiates yet. Those would come from Asia, were they even known in this era? And at what point would opium have made its way west as far as Greece?

In his Histories, Herodotus relates the tale of the Scythians' practice of smoking marijuana. My sense of this account was that Herodotus regarded the smoking of marijuana as one of the Scythians' unique customs. in other words, it does not seem to be something that he Ancient Greeks regarded as common or 'normal'.