Hinnom/Ashdod/Gath center around the concept of a "few mighty men," that is, small armies that are much tougher than mere numbers would indicate. I haven't played much with Hinnom or Gath because I dislike blood nations, but Ashdod has a nice smattering of Earth/Death/Astral/Fire, with a touch of blood and nature in the summoning tree, and quite a lot of overall versatility. Here are some thoughts from my few days of playing around with Ashod.
In order to take the concept of a "few mighty men" to its logical extreme, i.e. one Adon soloing indy provinces on his own at the beginning, it is absolutely essential to have an E10 bless and some level of regen, preferably 10% (N6). This gives you functionally zero encumbrance. You might think that E9 is enough, but fatigue mounts quickly when your lone Adon is trying to solo 60 indies and with an E9 several Ahiman Anakite guards will be necessary. With E10N6 you can expand as quickly as you can accumulate Adonim. Be sure to take Heat-3 scales because the extra +2 encumbrance in Heat-3 provinces will not affect your Rephaite troops (which is everyone except humans and Edomites) as they are all 50% heat resistant.
Your units are pretty decent. The top-line recruitable-anywhere troop is the Bashanite, with 40 HP to the Gileadite's 35 and 26 damage to the Gileadite's 21 (but worse repel). The Bashanite is superior against most foes because of the additional chance of one-shot-kill, but the Gileadite is quite decent and has excellent morale. (Note that the Gileadite shows up in PD, 1 Gileadite and 1 Edomite per 2 PD, and 1/2 Gileadite Archer per 2 PD over 20.) Mix in human slave warriors to improve force density (Size 4 Bashanite + Size 2 human = full square) and reduce enemy defense. I haven't thought of a use for the Edomites or poison spear warriors yet--generally it's better to kill things outright than to poison them slowly, and the Edomites have fairly bad stats and poor morale. The Gileadite Archers have a bow that does 17 damage, but because of their high resource cost and gold cost, against all but the heaviest troops you're better off using Edomite javelineers and/or human slingers. (The fluff text notes that the Gileadite archers showed their worth against the Abysians by picking off their mages at long range. I can buy that, but it's a niche use.) Overall, Ashdod troops are fairly expensive and easily swarmed, and you'll outright lose any pure slugging match against a conventional-arms power like EA Ulm. However...
Ashdod troops have high HP and decent (13) Prot. They make excellent blockers for Ashdod's nifty battlemages, the Zamzummites and Rephaite Sages and Talmai Elders. Ashod can forge the Skull of Fire and Flame Helmet to get up to F5 reliably. They can forge Earth Boots to get E4, and in the late game can bootstrap to Bloodstones and E5 via Banquet for the Dead. They can forge Skull Staffs and Skullfaces to get up to D6, and forge Starskine Skullcaps and Crystal Coins for up to S5. Any of these limits can actually be exceeded because Ashdod can also forge Rings of Sorcery and Wizardry. (S3 Talmai Elder forges Starshine Skullcap, gives it to an S1E2 Zamzummite, which is 1 in 8, who forges a Crystal Coin and gives it back to the Talmai Elder who is now S5, and forges a Ring of Sorcery, which is used with the above to forge a Ring of Wizardry.) 1 Zamzummite in 4 will have Astral magic so he can participate in communions with 1/3 Rephaite Sages and 1/3 Talmai Elders, but it's more likely that large communions will happen by way of Zamzummite-forged Crystal Matrices. Fire magic is especially interesting to Ashdod because almost all troops are resistant to fire and have good armor. Evocation magic in general is pretty solid for Ashdod, because Zamzummites are sacred (I mentioned an E10 bless?) and all mages have decent precision (10 except for Talmai Elder's 9), and there won't be much damage to Ashdod's large (i.e. widely-spaced), high-HP troops.
Here's a breakdown of Zamzummite randoms and what they can be used for. Zamzummite base is 1E2D + 100% (E/D) + 100% (E/D/S/F).
1/8, +FD: Banefire. 1/8, +FE: Magma Eruption. 1/8, +SD: Nether Darts, or thugging, or communions. (See below.) 1/8, +SE: Gift of the Heavens, or communions. 1/4, +ED: Terror, Leeching Darkness, skelly spamming, or thugging. 1/8, +DD: Cloud of Death.
Thugging is also an option. For starters, as mentioned, an Adon with the right bless can solo indy provinces naked. Talmai Elders have forge bonus (15), and Adonim and Talmai Elders have full slots + 1 extra misc slot. Zamzummites can do Summon Earthpower/Invulnerability/Soul Vortex, or Body Ethereal/Ironskin/Soul Vortex, depending on randoms.
One particularly interesting possibility is a linebacker communion (kudos to Baalz's Guide for the term). Give four or five Slave Matrices (5 earth, 5 pearls) to various Adonim and/or Zamzummites. Have the communion masters cast some or all of the following: Personal Luck, Summon Earthpower, Invulnerability, Ironskin, Fire Shield, Phoenix Pyre, Soul Vortex. With high HP and a good bless they will be much more durable than most linebacker communion thugs. Zamzummites have fairly poor attack ratings, so either give them good weapons or else... Boots of the Behemoth (5 gems). Size 4 tramples size 2 twice per turn, but fortunately between E10 bless and Summon Earthpower you'll have reinvig 9, which is more than enough to overcome the 6 fatigue you'll pick up per turn of trampling (Zamzummite has enc 3 naked).
Supply is one weak point of Ashdod troops. Most troops have at least Gluttony-1, and Ahiman Anakites have Gluttony-5 and take 9 supply to feed. I'm not sure what wasteland survival does because I definitely had troops starving in wastelands. Perhaps it reduces the requirements slightly but it's still painful.
And of course there are a lot of great national summons, like the Arel with Healer (50) and the Ophanim and Chayot (Call Merkavah). Call Merkavah is almost unspeakably cool. 4 Ophanim + 1 Chayot commander roll right over entire armies.