Duryodhana went to Heaven first after his death. Yudhisthira saw him in heaven as the king when he entered there:
Arrived at Heaven, king Yudhishthira the just, beheld Duryodhana
endued with prosperity and seated on an excellent seat. He blazed with
effulgence like the sun and wore all those signs of glory which belong
to heroes. And he was in the company of many deities of blazing
effulgence and of Sadhyas of righteous deeds. Yudhishthira, beholding
Duryodhana and his prosperity, became suddenly filled with rage and
turned back from the sight.
And regarding other Pandavas and Karna, they were not present in heaven immediately, but had gone to hell. Messengers from heaven lead Yudhisthira to hell through an unauspicious path where he heard them screaming:
"Thus addressed, they answered him from all sides, saying, ‘I am
Karna!’ ‘I am Bhimasena!’ ‘I am Arjuna!’ ‘I am Nakula!’ ‘I am
Sahadeva!’ ‘I am Dhrishtadyumna!’ ‘I am Draupadi!’ ‘We are the sons of
Draupadi!’ Even thus, O king, did those voices speak.
But, if you are wondering why Pandavas went to hell, then it was just an illusion by Yama to test Yudhisthira and deceive him as he had deceived Drona about his son:
O son of Pritha, thy brothers, O king, were not such as to deserve
Hell. All this has been an illusion created by the chief of the gods.
O king, that desirous of doing thee good, I caused thee to be sent for having a view of Hell. Thou hadst, by a pretence, deceived Drona in the matter of his son. Thou hast, in consequence thereof, been shown Hell by an act of deception. After the manner of thyself, Bhima and Arjuna, and Draupadi, have all been shown the place of sinners by an act of deception. Come, O chief of men, all of them have been cleansed of their sins. All those kings who had aided thee and who have been slain in battle, have all attained to Heaven.
But you might be wondering why Duryodhana got to go to heaven. This is because, he fought like an warrior in the battle and died a khsytriya's death. And as Krishna had told in Bhagavad Gita, if one dies in the battle doing his duty, then he goes to heaven:
hato va prapsyasi svargam [BG 2.37]
- If you get killed in battle field, then you'll attain heaven.
And those whose sins are more enjoy heaven first and then enter to hell. So after death they attained heaven. And after having spent their time there they then proceeded to their respective abodes. Like you have said, Karna went to surya loka, Yudhisthira entered into the God of Righteousness and so on. The 5th chapter of Swargarohanika parva mentions all these.
Reference: Mahabharat, Swargarohanika Parva