Odds - the ratio between the amounts staked by the parties to a bet, based on the expected probability either way.
Chances - a possibility of something happening.
while the two words are almost identical, you find the difference in what the speaker is trying to say. This being the case, some times they can be used interchangeably, some times they cant.
Lets take a look at your examples:
The odds/chances are good that he'll survive.
Chances, in this case meaning *probability* (odds would be betting against something
.
What are the odds/chances of winning? can be used interchangeably
What are the odds/chances that they'll be there on time?
chances because you are asking the probability of being on time happening
Smoking increases the odds/chances of getting lung cancer.
Chances *probability of something happening*
The odds/chances are in our favor.
*Odds because its the ratio of good or bad things happening*
She knew that the odds/chances were against her. Odds ^same as above^
It could rain tomorrow, but the odds/chances are against it.
*Odds ^comparatively speaking*
The odds/chances are in favor of a major storm this weekend ^Odds comparative^
//** I know this is very difficult and confusing and alot of that confusion comes from how much the words have changed throughout time to mean different things in a colloquial setting. I could teach an entire 60min class on this topic, but I hope this has helped shed some light on the subject! good luck **\\