The thing with the Kraxis is that if you are playing on a low dificulty you can just pursuade the enemies capitol (or most advanced city) since it will "only" cost 1000 gold. Same thing on higher difficulty is, it most often is too much money to spare.

Be careful though: If you do not send troops to that city or rush a unit production there it WILL be comquered back very easily.

However you can use the 100 gold bribe on enemy units to win fights you normally wouldn't. BUT you have to get close to them (melee) with your sovereign so its not an easy move. Also it most likely only works on humanoid units and not dragons or wild beasts.

In the beginning Karavox has the Water 1 spells most notably "Illumination" (I think this is the wrong name) which will provide +1 Research in your enchanted city. It is super useful early on! Use it on each of your cities if possible.

You also start with the "Spikes of Krax" which are equipped with gear you have not yet unlocked/researched. Be careful not to lose them, they are good damage dealers and tanks if you cater to them well.

Your special ability "Fortify" along with those troops (do train those whe possible), your city defense bonus and your +8 Defense when under 25% hitpoints allows for very hardy troops and near impenetrable fortresses. With a good defensive force and your research bonus you can easily try to move towards tech spell victory. (Although you would have to focus all cities towards research, but the one which you will want to defend after you researched the techs. Make that one a fortress. It should build all the buildings you need for the Forge which will eventually win you the game if you can defend against your opponents with your super strong defense.

Try to position your cities at chokepoints, so your opponent can't surpass them and defend them well.

Another possibility is to go towards a Treaty Victory, but that will only be possible if your army is well endowed but you never attacked someone. As long as your power rating is higher than every other power rating the AIs will be eager to ally with you.

In my opinion your troops strength is not the offense, but the defense so a conquest victory is normally not my goal, but as any faction thekrax can do that as well. If you surpass your enemy in strength you can crush him, your city pursuasion can be used tactically to get rid of an opposing thread without much of a fight. Notice that if you buy an opposing city, its stationed troops will be right on top of it, without its cities defense.

A quest victory is really situational since you normally do not have instant access to the region in which it is located. If you have, it is always there, but should not be attempted without a force of at least a few companies of high initiative troops with high damage.

Also do use the customization options to make your own troops. Many troops you can create are that much better than the proposed ones. Focus on high initiative high damage troops when going for (con)quest victory and on armored pike shield troops when wanting to go for the defensive tactics.

It is most useful to have ranged units along with your spear+shield ones. Those spear units will fortify in front of your ranged units (preferably mages) and cover them with their increased dodge as well as dealing safer dmg with the increased accuracy. The AI cannot  run thorugh those units, because of their zone of control meaning anyone passing along your units has to stop if it is crossing inside a 1 radius

I recently played a Kraxis game on high difficulty. I generally don't worry too much about which victory to aim for; all of them are achievable if you become powerful enough. As N1ghthavvk notes, the quest victory assumes you can get access to that quest, but apart from that it's more or less a matter of taste and how a particular game goes.

I never used the bribe a city power. On high difficulty it was just more gold than I ever had; by the time I could conceivably have saved up 1000 gold I had a strong enough stack that I could take any city I wanted to.

The bribe a unit power on the other hand was quite useful. It only works on Trained units, but my basic tactic was to more or less win a battle and then decide which Trained unit I wanted to take over. As this was on high difficulty the AI units generally had much better stats than my troops, so this was useful in two ways: after I'd killed all the easy targets I could eliminate a dangerous unit (generally very high hit points and armour) with one move; and I then had an extra quite powerful tank type unit to play with for the rest of the game. Towards the end of the game this was less useful because I could kill the AI Trained units and could build better trained units (mounted, higher initiative) myself. But it definitely had its uses allowing me to win battles with fewer casualties and preserve a good stack in the middle of the game.

Assuming you want to use the Kraxis special abilities it makes sense to build Towns, have trade treaties, put Towns on gold production, and everything else you can do to maximize your gold production. Not at the expense of building a balanced and defensible empire, but when I played Kraxis I aimed harder for a gold surplus than I would normally; I put the taxation level maybe one level higher than I would have done otherwise, for example. Having 100 gold available for any battle against the AI with your sovereign (so you can bribe a Trained unit) is a reasonable goal.

The Fortify ability is most useful if you can let the enemy come to you. I generally win my battles with my mage, so the basic tactic was to set up a wall of Fortified units to give my mage time to cast battle winning spells. With shields and on defend your troops can become very hard to hit. I assume the same tactic would also work with ranged troops. There are variations on this, e.g. move expendable unit next to dangerous unit, put it on Fortify and Defend, the dangerous unit will use its attacks on your unit until your unit is dead or until you move another unit next to it. Occasionally I also found it useful to protect a hero who was vulnerable to ranged attack, so I would move the trained unit off the Fortified tile and move the hero onto it. Fortify does recharge over several turns (5?) so it can also be useful at the end of the battle as you swarm around the last tough enemy unit.

If you use a sovereign wraith dodge build, a kraxis champion is pretty awesome with mass ranged behind. Move Forward/kite backward to a good position, build fort, move out, let the mass dodge craziness begin. You can do this without sacrificing turns/initiative if you are clever about movement and positioning. 

How does the "pay 1000 gold for a city" ability work? Must I be at war with the faction I "buy" the city from? If not, will this put me at war with them? Do I suffer unrest as if I had conquered the new city?

Thanks in advance