Hi Laura,
The first number (1.82) is the number of multiplicative interaction [OR11/(OR10*OR01)], the second number (6.34) is OR11 or double exposed OR. You can use the first code (logistic case sex colgrad age i.snp##i.smoking) for all your calculations if you feel more comfortable with coding that way. With the right coefficients in your nlcom command, you should be able to get the same answers.
In HW6, the code to answer question 7 will be "logistic case sex colgrad age snp#smoking". This code gives you the OR’s for each cross-classified exposure group, whereas the code to answer question 8 will be "logistic case sex colgrad age snp##smoking" where you get the multiplicative interaction.
I hope this helps,
Monica