I don't know how your playing but I think I might know what you are doing wrong. I'm gonna guess your trying to build units your can't really afford to build. Gildar is hard to come by but people are not and thus it's better to focus on getting more units out then trying to get the best you can field which it sounds like your doing since you said "no matter how strong of units I research, they sap my money and I get obliterated the second someone declares war on me".
That being said here are some basic strategies I use when playing the game I haven't really had a problem deal with the AI, in fact I consider them to be a push over.
1) Every city should be training troops at ALL times. Even if it's only peasants they should be training something. If you can't afford to then you need to build cheaper units. The only time this rule doesn't really apply is late game when you have 6+ cities and a HUGE army already. But your first 3-4 should always be training something early game.
2) Only build what your really need or can afford, especially early one. A lot of the buildings give +% which is fairly worthless in a city that only produces ONE of that item. Build those in cities that are near the resource that produce them so you'll actually get some worth out of them. It's easy to spend a ton on those buildings early on and then not have enough cash to follow rule 1. You can build them though if you have plenty of extra resources as long term every little bit helps.
3) First Military research every game should be the one that let's you train Parties (units of 4). As a simple Party of Peasants cost 16 gildar and 4 materials but has 12 ATK and 20 HP. A couple of these can easily handle wandering monsters which give you gold for killing them. I usually build Pioneers first and do this as my first R&D of the game so I don't even bother with Individual peasants.
4) Camp nearby forest for wandering monsters to XP & Gildar grind. It seems that any forest not in a zone of influence has a chance of spawning enemy monsters in it. In some of the larger forest areas it seems like there is almost always 1 monster unit there for me to kill. A small army of peasants will easily earn you more then it cost to field them but you will loss a few from time to time.
5) Send units back to your cities to heal them especially early on. Hit and run tactics against monsters are really important early game. Since leveling up even your basic peasants gives them extra HP and thus they can last even longer. I tend to have a line of new units heading towards the front and injured units heading back to closest city.
6) Monsters don't seem to spawn in side your area of influence but will wander into it. So once you've spread your influence out over a forest area and much of the nearby land it's usually safe to leave only a small group guarding the city while the bulk of your army guards the borders.
7) Imbue new Heroes you want to be casters at level 1. This way every time they level up they can spend it on essence. High level casters are very valuable especially if you know some good tactical spells.
8) Taking the Summoning SOV route helps a LOT. Pick or make a SOV with the summoning book then following rule 7 to get a lot of heroes with large pools of mana you can field a fairly impressive army for pretty much free. Each champion can only have 1 of each summon monster type but if you have 3 champions, including SOV, then you can easily summon an army of 9 units that are fairly powerful pretty early on. And army which is completely disposable since the only thing they cost is Mana and the time it takes to regen the Mana. About 15 turns worth since there are 3 summons that cost 5 mana each. Later ones cost 8, 10, 15, 16, and 20 Mana. But if your level your heroes they should have plenty of mana to summon these nasty monsters that are in the mid teens or higher with ATK/DEF.
9) EXPAND! You want to grab resources early but only the ones that are actually important to your early growth. Focus on Gold, Materials, and Food resources first. Metal and Crystals are nice but their only real use is advanced units which you need to research the equipment for first. The Arcane and Tech Libraries are also nice to get your research kicked off faster. Shards are among the LAST things you should worry about as they cost 100 gildar to setup on. Most resources nodes are expensive to build on which is why you wanna focus on only building what you need. Like if you have plenty of food you may set a city near some fertile land but don't build the farm till you actually need the food as those resource are better spend else where. This all goes back to rule 2.
10) Don't rush up the Military Equipment tech tree. The more powerful units easily get very expensive with all the fancy equipment and if you don't have the Metal and Crystal of field them it doesn't do much good to research them. Not to mention their Gildar cost is fairly high as well and unless you've built a good income base you won't be able to produce them in reasonable numbers to make much difference. Instead focus on unit size and experience. Groups of 4, 8, and 12 units are much better then an uber equiped unit. Also vets gets 50% more HP while Elites gets 100% more. So for extra time you get a unit that cost the same but has more HP. This is where having every city building helps as it negates the extra time to build. Like one game I was building units that took 40+ turns to make but had 8 cities so on average I could make one every 5 turns.
11) The Adventuring Tech tree has a path that unlocks more resources. The early ones are handy to get as they reveal more Gold, Material, Food, and Metal. Also once your fairly secure in your area with a few units of troops and the forest monsters are under control it's good to research questing. This will reveal more questing locations and goodie hunts to be looted. I'm not 100% on this as my testing is limited but it seems to spawn a ton within your area of influance so the larger your area of influance is the more that seems to spawn. So holding off on questing research until you have a few cities with large circles of influance can be handy. I had dozen of locations spawn when i research it and had 8 large cities.
12) Caravans don't give you extra Gildar/Materials like they did in Beta. Now it seems they only give a bonus to food production and build the roads. So pretty much choose if you want them for the roads or the food boost. Some of the outer edge cities that are no where near a food city I just connect to the nearest city to form a road network to help move my troops to the front faster.