"Rama, Orach Chaim 656:1, rules that one must spend up to one-fifth of his assets on order to fulfill a positive mitzvah and his entire fortune in order not to violate a negative commandment." (source) As for negative commandments that are violated by passivity--such as the commandment that you may not allow someone else to die--there is dispute about whether they are considered "positive" or "negative" commandments for the purposes of this question. R. Yair Bachrach, in Chavot Yair no. 139, considers this example a positive commandment, which one must spend up to one-fifth of his assets to fulfill, whereas Rivash (no. 387) considers it a negative commandment for which one must spend one's entire fortune.
As for illness: a choleh or sick person is considered exempt from some mitzvot, notably fasting, but Rabbinical opinions seem to vary substantially as to the full extent of a sick person's exemptions from mitzvot. Some opinions are discussed here. Very generally, it seems that a sick person is often exempt from positive commandments but rarely negative ones. (CYLOR if it applies to you, of course...)
The question of whether one should make himself ill--including, perhaps, emotional illness--in order to fulfill a commandment is another question of debate, but at least one authority suggests that "Since one is not required to spend more than a fifth of his assets for a mitzvas aseh then certainly one is not required to make himself sick." Whether it would be permissible to do so (i.e., to make oneself sick in order to perform a mitzvah) is still unclear to me.