The opponents you are facing are special Encounters in the campaign. When you did your first encounter, there should have been a popup telling you that Encounters are specifically designed this way in order to help you improve your skill at facing specific strategies. These matches are specifically labeled with Encounter in front of the name of the match, like Encounter: Disturbing the Nest and Encounter: Face of the Ghoulcaller.
Encounters will always play out the exact same way. For example, during the Encounter Stampede!, the AI will always play a Willow Elf on Turn 1, followed by a Runeclaw Bear on Turn 2, and so on.
Encounters also, as you have noted, have decks that are exempt from the limit of 4 of the same type of card.
The Planeswalkers you face in the campaign and other opponents, like Odric, have decks that are subject to the 4 card rule. Note that the game with them will also be different each time you play, in contrast to the Encounters, which always play with the same order, use the same strategies and same cards.
The deck that I have had the most success with is as follows:
Jace's Phantasm (2), Visions of the Beyond (2), Tome Scour (2), Unsummon (2), Hedron Crab (2), Counterspell (2), Into the Roil (2), Jace's Erasure (2), Mind Sculpt (3), Crippling Chill (3), Sands of Delirium (1), Sword of Body and Mind (1), Clone (2), Sleep (1), Icy Manipulator (2), Telemin Performance (1), Archive Trap (1), Body Double (1), Traumatize (1), Scalpelexis (1), Isleback Spawn (2), Chancellor of the Spires (2)
The breakdown looks like this:
Mana 1: 10
Mana 2: 9
Mana 3: 5
Mana 4: 5
Mana 5: 5
Mana 7: 4
Sub Total: 38
Total (inc Mana cards): 65
The focus of the deck is to attack the other player's library, while drawing cards. Half of the spells in the deck are low-cost (1 or 2 mana) to allow for a constant assault. This also means you should be able to start right away.
I've ignored cards that allow the opponent to draw cards, as I found this to be a great help whenever I play against Jace's deck.
In answer to the second question, there are several ways to modify this deck, but I would advise staying as close as possible to the 60 card deck minimum.
A full listing of available cards (by deck) can be found here
Best Answer
Krenko's deck is all about the speed, but his creatures are fairly weak, so there are a few different avenues of attack that work against him.
Strategy 1 - Use the other swarm deck. The Peacekeepers deck is almost as fast as the goblin deck and has larger creatures in it. You are looking to gambit off your creatures to prevent Krenko from reaching critical mass, before sealing it with your larger creatures and those with flying. You also want make sure that you kill off/exile the direct damage goblins as soon as they show up.
Strategy 2 - Put the brakes on. This one is for the red and black decks. It's also the best way to take the goblin deck down in multiplayer, as well. You slow the deck down till you can get enough mana to cast a few game enders. Basically, you are going to trade some of your life point total, while you kill the biggest threats so that the deck is out of cards in hand when you get to that magical 6/7 mana range. You can afford to lose about 8 life without putting yourself in one turn killed territory. You also want to save your board clear spells until you can take out 3 or 4 goblins, directing your single killers at the big threats of the goblin chieftains and the mob boss.
The biggest thing that you need to do is keep the pressure on at all times. The goblin deck is super aggressive, but it has little to no defense. If you can outlast the savagery or put it on the defensive, you are almost guaranteed a win. You also want to kill a goblin off whenever you can because once that deck hits five goblins out, you are looking at a terrible time after that.