How does Catch-22 satirize the absurdity of war and the perspective of justice?

Heller exaggerates the absurdity of his characters' actions, presents war as a battle against one's own side rather than a foreign enemy, and subverts the principles of justice to satirize the nature of war.
The absurdity of war is a major theme throughout Catch-22. While the story takes place during World War II, the real battle of the novel is not between the Allies and the Axis powers but rather with the individual men and their superiors. Throughout the story, the number of flights that the men must fly in order to leave is continually raised, and within that dilemma lies the central paradox:

There was only one catch and that was Catch-22, which specified that a concern for one's safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but if he was sane he had to fly them. If he flew them he was crazy and didn't have to; but if he didn't want to he was sane and had to.

The quiet, illogical brilliance of this theme is highlighted throughout in characters such as Aarfy, who leaves his position in the middle of an attack to taunt Yossarian and nearly gets them all killed; and McWatt, who flies too close to the ground for fun and accidentally kills Kid Samson in doing so, only to commit suicide by flying his plane into the side of a mountain. These characters show the dubiously "sane" nature of those who don't mind flying missions. 
The absurdity of war is highlighted further in the command structure of the base itself. The officers constantly angle for promotions by ridiculous and sometimes lethal means: Whitcomb, the chaplain's supposed aide, is so proud of his condolence letters that he hopes men will die to make them more prevalent, and the colonel raises the number of missions in the hope of impressing those above them. The enemy is feared, but the immediate danger is within their midst. 
Justice is mocked frequently. In the course of an unsuccessful bombing run, Yossarian repeats the route to drop the bombs; unable to decide if his actions warrant punishment, he is instead promoted. Similarly, the chaplain is accused of being Washington Irving because he didn't have the same handwriting as the letters. Questioned in a room full of instruments of torture and summarily pronounced guilty (because if he was innocent he wouldn't have ever been thought guilty), the chaplain finds himself let free. These actions so obviously lack any sort of reason that they mock the very notion of justice.
All of these actions work well on their own to satirize the absurdity of war, but Heller heightens the effect by exaggerating the characters' actions to the breaking point. Milo does not merely siphon resources away from the battlefield but begins his own corporation with them and feeds the men like royalty on damask tablecloths with kidnapped skilled Italian waiters; he does not merely make a bad investment but buys the entire crop of Egyptian cotton to no avail. Orr does not merely ask someone to injure him to avoid battle, but convinces a whore to beat him over the top of his head with a heeled shoe until his skull fractured. The characters are caricatures, and as such the absurdity of the novel is heightened.