Can Ogre clerics use Purify Food and Drink on humanoid characters to cure them as humanoid creatures are regarded as food in Ogre culture?
Similarly, can Ogre clerics use Create Food and Water to summon a halfling teammate?
Before I get into the details, consider the general principle that there are no secret rules in D&D 5e. So, always be suspicious of a reading of any feature that seems to allow additional benefits for only a small subset of users, especially if those additional benefits are not explicitly stated anywhere. Anyway...
All nonmagical food and drink within a 5-foot-radius sphere centered on a point of your choice within range is purified and rendered free of poison and disease.
Rules as written, whether a humanoid eating character could use this spell to heal other humanoids of poisons and diseases really depends on how you choose to define 'food and drink'. These are not game defined terms, so it's up to DM to make their own call or ruling. Can living breathing humanoids be considered food? That may come down to whether you'd call a cow food, or whether it would have to be a steak first.
Rules as intended, this should definitely be disallowed - it's a huge exploit. To illustrate this just compare the effects with Lesser Restoration. Lesser Restoration is a 2nd level spell that lets you cure just one creature of just one condition. Purify Food and Drink is a first level spell, which can be cast as a ritual, therefore not expending a spell slot. Ruling that it could be used this way would allow it to cure every poison or disease affecting every creature in a five foot radius.
You create 45 pounds of food and 30 gallons of water on the ground or in containers within range, enough to sustain up to fifteen humanoids or five steeds for 24 hours. The food is bland but nourishing, and spoils if uneaten after 24 hours. The water is clean and doesn’t go bad.
Rules as written, it's just about arguable this spell could be used by a humanoid eating character to create an adult halfling. If you have already ruled that living humanoids can be considered 'food', which I would not recommend, then, by weight creating a living adult halfling is possible (they weigh about 40 pounds).
Would a halfling be bland and nourishing to eat? Nourishing, maybe but bland seems unlikely - however as far as I'm aware there's no published material that discusses how the playable races taste. If your DM has already allowed you to consider a living halfling 'food' it seems unlikely that this will prove a sticking point, with a lack of actual evidence to the contrary available.
Rules as intended, however, once again this is a massive exploit. The spell text states that the 'food' you create 'spoils if uneaten after 24 hours' - that doesn't seem like an accurate description of a happily functioning, living and breathing humanoid to me. The spell text therefore probably isn't intended to describe living creatures.
Once again, comparison to other spells reveals how overpowered this is. There are lots of other spells that allow conjuring allies (for example) and they generally are fourth level or higher spells, and once summoned the allies stick around for about an hour. If allowed, Create Food and Water, would undercut all of those spells. It would become a third level spell that allowed the creation of a halfling ally that could last a day until they started rotting (or years if you then cast Purify Food and Water on them!). Either way, by allowing all of this you'd have moved firmly into fairly ridiculous homebrew territory.
All other spells that are capable of summoning companions provide guidelines for the statblocks that should be used for those companion. Here you'd need to make them up - which should be another indication that it's not an intended use of this spell.
3. It's not about the Ogre
A final caveat - as I see it this question isn't really just about an ogre. The ogre is (ironically) the thin end of the wedge.
As demonstrated in this Reddit thread an NPC Ogre wielding these spells could be a hilarious addition to your campaign. However, what's good for the goose is good for the gander and if an NPC can do it, soon your players may want to do it too.
Ogre's aren't (at time of writing) a playable race but there are playable monstrous races which could be argued to eat other humanoids. Taking it further, in an evil campaign, any PC could declare themselves a cannibal. Or, in a good campaign, they could take the Haunted One background and say that as a child their PC got lost in the wilderness and ate their friend, after they'd died, in order to survive. They've never told anyone but the memory still tortures them and they can't shake the idea that ultimately everyone around them is made of food.
Basically, if you let an Ogre NPC do this in your campaign, it'll be hard to justify disallowing other characters - including PCs - from doing it too.
You can not use Purify Food and Drink to remove poison and disease from a humanoid as a humanoid is a creature, not an object. By this logic, you also can't use Create Food and Water to create a halfling as a halfling is a creature, not an object.
Food and drinks are objects, not creatures. We know this because the Player’s Handbook refers to food and drink as objects.
From page 190 of the PHB:
Interacting with Objects Around You
Here are a few examples of the sorts of thing you can do in tandem with your movement and action:
- stuff some food into your mouth
- drink all the ale in a flagon
This provides evidence that ‘food’ is an object as it is listed as an “object around you”. Thusly, if ‘food’ is considered to be an object, a living humanoid can not be considered ‘food’ as a humanoid is a creature, not an object.
A flagon of ale, a type of drink, is also considered to be an object. If food is an object and a flagon of ale is an object (and potions are also considered to be objects by that list in the PHB), we can safely assume that a ‘drink’ is also considered to be an object.
A possible loophole might be to say you create a deceased creature which, according to Jeremy Crawford, is an object. If a corpse is an object, it can be food.
However, as a living halfling is a creature, you can not use Create Food and Water to create a halfling teammate. If a deceased creature is considered to be an object, you could use Purify Food and Drink on a humanoid corpse but not a living humanoid.
You may be able to achieve both of the desired effects listed in the question by casting multiple spells.
An interesting thought I had:
If you wanted to use Purify Food and Water on a living human, you first would have to kill them, cast Purify Food and Drink and then cast Revivify on the corpse. The result would be a living humanoid who has now been cured of any disease or poison that was ailing them.
However, if you used Create Food and Water to create a deceased halfling, you would not be able to use Raise Dead or Resurrection to bring it back to life as it was never alive to begin with. Thusly, there is no soul that could rejoin to the body as no soul ever left it.
Note that objects can carry the poisoned and diseased conditions. This is evident as the descriptions of both Resurrection “This spell neutralizes any Poisons and cures normal Diseases afflicting the creature when it died” and Raise Dead “This spell also neutralizes any poison and cures nonmagical Diseases that affected the creature at the time it died” imply that a corpse can contain a poison or disease. If a deceased creature is considered to be an object, objects therefore must be able to carry the diseased and poisoned conditions.
The way I see this, it's not about rules but about semantics. The question being: What constitutes food?
For starters, and taking the definition of food from the PHB, food constitutes something a character needs to consume to survive.
A character needs one pound of food per day and can make food last longer by subsisting on half Rations.
Given the ogre in question considers raw living humanoids as food, there needs to be something that's subjective to the ogre character: the determination to consume such beings as food for his own benefit, foregoing any benefit towards the consumed being.
Could the caster cure diseases and poison to these beings using the spell you mention? Well, yes, but only if those effects could be transmited to them if they would consume them.
In a strict sense, not all diseases and toxins can be transmited by consuming something that has them. Maybe the inoculation method is other than ingestion or the disease is species sensitive or not contagious at all.
So, since food is defined by the one who consumes it, diseases and poisons are also related to what affects them and not the consumed being in question.
In any case, I understand this is far from the intended use as it's commonly understood that animals need to be dead to actually be food. Also, you don't summon an ally if you're conjuring food. You're no ally of your meal, it's pretty much the opposite.
 The relevant rules for Diseases and Poisons are in the DMG (256-258) as pointed by @Akixkisu in the coments.
If you're about to eat an animal, you are only concerned with disease that could poison you.
However a rancher is concerned with diseases that will prevent the animal from thriving. For instance if a 100 pound calf has anemia, it's harmless to eat, but won't live to become a 500 pound cow worth butchering. Husbandry, keeping animals healthy to become future meals, is clearly beyond Purify food and drink's pay grade.
So that creates a "top limit" - the most the spell could ever possibly do is render the target not unsafe to eat right now.
Of course, "the dose makes the poison", so a poison dose may be enough to kill the target, but if the meal won't create enough dose to harm the caster's party... or if the poison concentrates in places like bones that you don't eat... that satisfies the objective of purify food and drink.
Of course, full-on disease science is not a thing in D&D, so to the players this just looks like poor odds.
Could you cast purify food & water on a humanoid? Sure.
I can't see any reason why a human cleric couldn't cast it that way. Whether or not the DM will allow it is another question, but purify food & water is fundamentally a healing spell.
What it wouldn't do is save a life. It would remove disease and poison, but if your arm was broken, it wouldn't heal that. I wouldn't even expect it to heal a cut (but it would expect it to cure septicemia). I've always interpreted the spell as being a lesser form of the "cure wounds" type of spells. It's intent is only to make something "edible." Nothing more. The fact that an ogre might prefer his/her dinner alive wouldn't change the nature of the spell, which isn't to preserve the pleasure of eating, but the alleviate the need to eat.
Think of it as a spell that ensures life, but not lifestyle.
Could create food & water be used to summon a humanoid? Sure.
But it's the edible parts (the flesh) that would be summoned, not the "spirit" or spark of life. The halfling might even arrive breathing! But it'd be a vegetable. A mindless body waiting to be consumed. It would be well beyond the intent of the spell to summon a creature useful in combat (other than as something to load the catapult with) using this spell.
The point of "purify food/water" is to ensure that food is edible without getting sick.
This means if you cast it on someone and then eat them - you have the guarantee that you won't come to any harm eating them.
You eat billions of bacteria every day - but if they're in your blood stream you'll die; you're able to eat a wide variety of venom's without suffering any ill effects; the list of things you can eat safely that will kill you if in your blood is actually very long indeed.
As such this spell could easily succeed; make the person edible; but not impact their life threatening problems in any way.
If I was the DM; I'd have the character make a wisdom roll to see if they'd be able to work this out - tell them it would be a waste of a spell slot if they made it; and tell them that it seems reasonable if they didn't; and then allow them to bin the spell.