kodiak spam

There's no real "counter" to heavy cruisers. In small numbers, you can beat CAs with simple numeric superiority. I prefer using my own CAs or bombers for this, but really the best is a mix of units -- usually LRMs + CAs + bombers.

But if he outnumbers your the best thing to do is to ignore his fleet and head for one of his fringe worlds and blow away his military labs. If he can't BUILD new CAs you have a chance and if you keep attacking his infrastructure he's going to have to either attack your infra or come back and defend. Either way, you hold the initiative.

Sixhits gives some good advice. I'll add to that that disabler cruisers can also work very well against enemy CA spam. If you're Vasari, get about a dozen Subverters with Distortion Field (don't let it autocast) and you can stun whole squadrons of CAs since they tend to clump up when attacking. If you're TEC, get you a sizeable force of Hoshikos, turn autocast off for repair and turn it on for demolition bots. Since Hoshikos are cheaper than CAs, you can get them in greater numbers and should be able to get enough to keep a significant portion of his CAs stunned.

Any Spam is easily defeated with a comparable economic backbone to the enemy.

Funny
I agree with Adama.

Could you elaborate on that?

the problem I have with disablers is they use ALOT of AM and once they run out they are nearly useless. Considering they will likely be at least half empty by the time they get there on the attack thanks to the loss from jumping, they don't seem very effective. The generator upgrades help, but not enough IMO. The AI also seems kind of stupid picking targets, which means more micro and more wrestling with the interface. I've never had any luck using them, even vs the computer.

The counter to 10 Kodiaks is 11 Kodiaks

Also, every race has a disabling cruiser - take it off auto cast and start hitting their HC's with it and you will severely cripple their ability to kill.... but now you have to kill them.... good luck with that - especially Kodiaks.

15 bomber filled carrier cruisers will help you rape Kodiak spam. Don't bother escorting them, make them a fleet of their own. Jump them in after your attack ships and disablers have tied up the Heavy Cruisers. Make sure the carriers have a hold position order so you can move them out fast if the HC's come after them.

You still have to work your disablers correctly, but the bombers will pop the enemy faster so you're less likely to have antimatter problems.

I can't speak for the other races, but if you have 10+ Subverters you should be able to stun an enemy fleet almost indefinitely without running out of AM - Distortion field is not a hard ability to micro - make sure you disable the autocast on their shield degradation ability as well if you really want to conserve. It only takes one subverter to put down a huge chunk of bunched up enemy ships, your other subverters can just sit there waiting for their turn. By the time you've worked through the subverter group - the initial disablers should've both cooled down and regained much of their antimatter - so you can start the process all over again.

Manually triggering shield degradation on the ship your bombers or assailants is attacking helps efficiency, it only takes one subverter to get the effect's maximum benefits.

But we don't know what race you're using anyway.

Probably the biggest problem with disablers by far. Mine tend to want to disable carrier cruisers instead of more important ships. More micro is required to get the most out of them.

A player with mobility, high production rates, and resources is the only thing capable of ruining a spammer.