Some aspects of the below were specific to Sweden while others common to most belligerents in the war. Where possible, I used Swedish examples as that was the OP's topic of interest.
Changes during the Thirty Years War
The long period of warfare seems to have been the cause for changes in how prisoners were dealt with. This is a general overview which works as a quick summary, but is not intended to reflect Sweden-specific items. Many of the topics are also covered in more detail below.
One symptom of the changes which took place during the 1630s and 1640s was the different treatment received by prisoners-of-war, in particular officers. Whereas simply soldiers who had been taken prisoner were often incorporated into the victorious army, officers were released provided they could pay a high enough ransom. During the early years of the war it was normally the commander of the regiment or other military unit which had captured the prisoners who received the ransom, but on the other hand, an officer who had been taken prisoner had to pay the ransom out of his own pocket. ... During the last years of the war it became normal practice for the rulers and princes for whom the various armies fought to pay their soldiers' and officers' ransoms when they were taken prisoner, or to exchange them for prisoners which their own forces had taken. Formal agreements were now signed which fixed the amount of money to be paid for each officer according to his rank. [Asch, 'The Thirty Years War']
Forced Labour
A late 16th century description noted forced labour in particular for Sweden:
The Swedes presented a problem, because the slave markets had declined there in the early fourteenth century, so there were no real instruments to deal with slaves. Perhaps the Swedes were only interested in the ransom business. Yet the ongoing settlement and forced labour policy of the Swedish crown hardly distinguished between military and other prisoners. The King of Sweden used prisoners like proper slaves-owner societies used slaves, especially in the mines, so for him, poor Livonians could have been just one resource among others. [Korpela, 'Slaves from the North']
Though a slightly different context, the premise is collaborated by Osieja in 'Indigenous Educational Policies in Yucatán and Swedish Lapland' which focusses on the Sami and notes how the King used them as forced labour in Nasafjäll silver mines after ore was discovered there in 1634.
Also, we have evidence of the counter-example to this where the Swedes taken prisoner at Poltava were used for forced labour by the Russians while being kept in captivity from 1709 until the Treaty of Uusikaupunki in 1721.
...on 1 July 1709, at Perovolochna in the Ukraine, 20,000 Swedish soldiers, their families, servants and artisans were marched into captivity. ... The majority of these would be released after the signing of the Treaty of Nystadt, in 1721. [Konstam, 'Poltava 1709']
Petersburg itself stands on what was once Swedish territory, and its streets were first paved by Swedish prisoners of war, thousands of whom perished in draining the marshes around it. ['Observations on the Policy of the War...']
Rank-and-File Exchanges
Prisoner exchanges seem to have been primarily arranged in official treaties. One such example (beyond Westphalia) is in the 1635 Peace of Prague (with Saxony). Wilson's 'The Thirty Years War' comments on Article 53 arranging the exchange of prisoners. I couldn't find a version of this online.
The cartels (or kartelle) which featured more in later prisoner exchanges are a 17th century development. Scheipers' 'Prisoners in War'] lists eight documented cartels before 1639, and these involved Spain, the Netherlands, and France. Perhaps Scheipers didn't go all-in with the documentation because elsewhere she writes:
Yet from the beginning of the 17th century exchanging prisoners with the opponent slowly became a common practice that considerably enhanced the captives' chances of survival. The system of prisoner exchange through bilaterally negotiated cartels continued throughout the 17th and 18th centuries. Prisoner exchange was a rational solution, since soldiers held captive were of no use to either side. Prisoners were either exchanged man-for-man or for ransom. Considerable efforts were made to specify "exchange rates" for different military ranks accurately. ... Ordinary soldiers were more likely to be induced to switch sides and join the adversary's armed forces if exchanging them was not possible.[Scheipers, 'Prisoners and Detainees in War']
Pressed Rank-and-File
Pressing captures rank-and-file into service on ones' own side was common for all armies of the time. Some Swedish examples are noted below along with a longer description of the process.
But the common soldiers, especially those raised in Germany, were normally neither ransomed nor exchanged: either they were freed, after swearing not to bear arms against the victor for a certain period, or they were encouraged to join the army that had captured them - a development often facilitated in the later phases of the war by the presence in every army of at least a few men who had fought on all sides and might therefore know the captives, and ease their scurples on transferring from one allegiance to another. In 1631, even the Italians captured by Gustavus Adolphus in his Rhineland campaign were welcomed into the Swedish army (though they deserted as soon as they reached the foot-hills of the Alps the following summer). [Parker, 'The Thirty Years' War']
The Swedes pressed entire imperial garrisons during their conquest of Pomerania and Mecklenburg in 1631, despite promising them free passage. The drawbacks swiftly became clear. Two-fifths of the Donauwörth garrison were forced into the Swedish army in April 1632, 'but being Papists of Bavaria, as soone as they smelt the smell of their Fathers houses in lesse than ten dayes they were all gone.' [Scheipers, 'Prisoners in War']
Supplying Prisoners
Scheipers' overview is good, but with no specific Thirty Years War statements:
In line with civil penal practice, captors were not held responsible for their prisoners' material needs. ... It was still common at this point [1710] for bankers to offer credit for governments to pay soldiers held on enemy soil. [Scheipers, 'Prisoners in War']
Officers
Officers were, perhaps obviously, considered a notch above the rank-and-file. Most officers had the expectation of a quick ransom and some ensured that this ransom would have to be paid by their King -- in a development from earlier precedent where officers would ransom themselves.
Sometimes prisoners were simply exchanged, as Torstensson (the Swedish general) was traded for Count Harrach (the Imperial treasurer). It was rare for a commander to be refused the chance of release, but it sometimes happened. Thus Gustav Horn, Oxenstierna's son-in-law, was kept in prison for eight years after his capture at Nordlingen in 1634 (although Maximilian of Bavaria did contemplate, at one point, bartering Horn against all the treasures plundered from Munich during the Swedish occupation; Stockholm, however, was not interested in the deal). [Parker's 'The Thirty Years' War']
Scheipers also details how parole was considered more and more an alternative to exchanges:
An alternative to exchange was release on parole. Officers were allowed to return to their home country or to reside on their own in certain designated "parole towns" on condition that they gave their word of honour to refrain from returning to the on-going conflict. [Scheipers, 'Prisoners and Detainees in War']
