I have been using these interchangeably, until today I was corrected, being told that one "参加活动”， not "参与活动“. I then looked up the definition, but it wasn't too helpful. How do I know when to use which?
Besides above answer, in oral Chinese, they don't have much difference. You can use either one.
参与，亦作“参预”或“参豫”。预闻而参议其事； 参与，also as “参预” or “参豫”. Listen something and talk about something.
参加。指的是以第二或第三方的身份加入、融入某件事之中。 参加 means join in something as a part of it.
So, mostly, 参与 has a meaning of organize some people and plan something, it often has a mean of initiative, such as: 他参与了此次军事行动的谋划工作。(Which means he is one of the commanders.)
As for 参加, which is just join in something as a guest or [third] part people, such as: 他参加了此次军事行动。(Which means he may be just a soldier.)
Besides, we often say : 这个事情我不参与. means do your own business, I don't care about it.
In my opinion,it is very difficult to identify the way how to use 参加 and 参与. It is the same as the preposition in English. Having no reason, if you don't do it as it should be, it's wrong.The only way to use it correctlly is to remember all the way to use it.
To me, sometimes I can find that there are some subtle differences related to emotional feelings between these two words, “参加” often tends to be more neutral in meaning, if you are not sure what kind of feeling you'd like to express on something, you can simply use “参加”, but if you want to express some relatively stronger feelings, whether positive or negative, you may consider using “参与”, take a look at these examples:
我昨天参加了班上举办的活动。 I took part in the party of our class yesterday.
被指控参与抢劫活动的有张三，李四和王五。 Zhang San, Li Si and Wang Wu have been accused of involving in that robbery.