For the giants question yes.

dgdata.zip\lua\sim\AI\AIGlobals.lua

Assuming this file is not locked to the dgdata asset we should be able to mod this.

CitadelUpgradeWeights = {
    # Fortified Structure
    CBuildingHealth01 = {
        Priority = -1,
    },

    CBuildingHealth02 = {
        Priority = -1,
    },

    CBuildingHealth03 = {
        Priority = -1,
    },

    CBuildingHealth04 = {
        Priority = -1,
    },

    # Building Firepower
    CBuildingStrength01 = {
        Priority = -1,
    },

    CBuildingStrength02 = {
        Priority = -1,
    },

    CBuildingStrength03 = {
        Priority = -1,
    },

    CBuildingStrength04 = {
        Priority = -1,
    },

    # Currency
    CGoldIncome01 = {
        Priority = -1,
    },

    CGoldIncome02 = {
        Priority = -1,
    },

    CGoldIncome03 = {
        Priority = -1,
    },

    # Blacksmith
    CTroopStrength01 = {
        Priority = -1,
    },

    CTroopStrength02 = {
        Priority = -1,
    },

    CTroopStrength03 = {
        Priority = -1,
    },

    CTroopStrength04 = {
        Priority = -1,
    },

    # Armory
    CTroopArmor01 = {
        Priority = -1,
    },

    CTroopArmor02 = {
        Priority = -1,
    },

    CTroopArmor03 = {
        Priority = -1,
    },

    CTroopArmor04 = {
        Priority = -1,
    },

    # Experience
    CPortalFrequency01 = {
        Priority = -1,
    },

    CPortalFrequency02 = {
        Priority = -1,
    },

    CPortalFrequency03 = {
        Priority = -1,
    },

    CPortalFrequency04 = {
        Priority = -1,
    },

    # Graveyard
    CDeathPenalty01 = {
        Priority = 3,
    },

    CDeathPenalty02 = {
        Priority = 6,
    },

    CDeathPenalty03 = {
        Priority = 10,
    },

    # Additional troops
    # Priests
    CTroopNumber03 = {
        Priority = -1,
    },

    # Angels
    CTroopNumber05 = {
        Priority = -1,
    },

    # Catapults
    CTroopNumber04 = {
        Priority = -1,  # angels and catapults were switched.
    },

    # Giants
    CTroopNumber06 = {
        Priority = -1,
    },

    CUpgradeStructure01 = {
        Priority = -1,
    },

    CUpgradeStructure02 = {
        Priority = -1,
    },

Not sure what -1 does, but if positive numbers do what you expect them to do then seem like the AI is set to pickup graveyard asap. 

@Peppe

Many thanks for this! Another rather noobish question: Do I need a particular program to access and mod .lua files? 

+1 Karma

P.S. If Sorian or other knowledgeable folks can help with this, I would be very grateful (and more karma to come!)

I am not in front of my gaming computer, so I can't really test anything.  However, I will try to mod this later today or tomorrow.  So, how might it work? Tweak the values that Peppe has found in the dgdata.zip\lua\sim\AI\AIGlobals.lua, using Notepad as the text editor.  Then save the modded file in Demigod\bindata\mods\lua\sim\AI\AIGlobals.lua?  Are do you need to put "dgdata.zip" somewhere in the installation path, which would seem odd (that is, to include a .zip file)?

I'm no fancy programmer type, but wouldn't be easier to just set a priority list. Like say, you want giants as your top priority so then a list would look like this:

Priests
Angels
Catapultasauri
Giants
Tower health #1
...

Having the list continue down as necessary. In this scenario they'd prioritize buying the units followed by everything else on the list in the order you specify.  Let's say they can't buy angels because the war score isn't high enough, so they'd skip down and buy tower health #1.

I'm just thinking back to Final Fantasy XII and how the gambit system worked. Set the priorities and triggers if need be. I'm partial to that style because then I can tailor my AIs to buy what I want, when I want them to. Including gear if so desired.

Sorry I'm not being real clear on this, but if you've played FFXII or any of Bioware's PC exclusive games (NWN/Baldur's Gate) or Dragon Age: Origins you'd understand what I'm talking about. Though admittedly this would be a far bigger list of scripted commands than what any of those games handled.