"Rama, Orach Chaim 656:1, rules that one must spend up to one-fifth of his assets on order to fulfill a positive [Biblical] mitzvah and his entire fortune in order not to violate a negative [Biblical] 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 Rabbinical commandments within certain parameters; as for Torah commandments, he may be exempt from certain 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.