All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
For the obligatory Hajj rites that you have missed, an atonement of slaughtering a sacrifice and distributing its meat among the poor in Makkah is required. For missing the stoning of the Jamaraat on the days of Tashreeq, it is required that you slaughter a sacrifice; for not staying overnight in Mina on the days of Tashreeq, it is required that you slaughter a sacrifice; for missing Tawaaf Al-Wadaa‘ (Farewell Tawaaf), it is required that you slaughter a sacrifice.
For whatever actions prohibited during Ihraam you have done, it is also required that you offer the expiation. If you did not make the first Tahallul (minor terminating of the state of Ihraam), then you have to offer an expiation if you applied perfume, wore sewn clothes, cut your hair or your nails. You have to make expiation for each act by either fasting for three days, slaughtering a sheep and distributing its meat among the poor in Makkah, or feeding six poor people. If you had sexual intercourse during the state of Ihraam before the first Tahallul, then your Hajj is invalid and you are obliged to make up for it the following year and slaughter a camel (or a cow) and distribute its meat among the poor of Makkah as an atonement (Fidyah).
The first Tahallul takes place when the pilgrim performs two of these three Hajj rites: throwing the pebbles, shaving the head and performing Tawaaf Al-Ifaadhah and Sa‘y. The second Tahallul (major terminating of the state of Ihraam) takes place when the pilgrim performs the third of these rites.
If you made the first Tahallul, then sexual intercourse was the only remaining prohibition. So if you had intercourse after the first Tahallul, then your Hajj is not invalid, but the state of Ihraam is invalid; therefore, you have to assume the state of Ihraam from outside Makkah, perform Tawaaf Al-Ifaadhah and then Sa‘y, and in this case you are obliged to offer the expiation.
However, if you did not have intercourse but engaged in Mubaasharah (i.e. lesser forms of intimacy like caressing, foreplay, kissing, touching and so on) after the first Tahallul but before the second Tahallul, then scholars held different opinions concerning this. Based on the view that it is prohibited, the expiation is required as with the other prohibited acts during the state of Ihraam that we mentioned above.
Allaah Knows best.