While an illness might be involved your description sounds a heck of a
lot more to me like they have gotten into a poison.

Use the resources in
http://www.aspca.org/pet-care/poison-control/

Including looking at plants, meds, human foods, and more because there
are a lot of things found in many homes and yards that are poisonous
rather than just the two you have mentioned.

[Posted in FML 7797]