连续 successive; continuous; consecutive
陆续 in turn; successively; one after the other
接连 on end; in a row; in succession
一连 in a row; in succession; running
From what I've read, 连续 is the most widespread term and would be the most accurate word for 'continuous', especially in science, as I have a book called 连续时间金融
From examples, 陆续 is closer to 'one after the other' or consecutively
I can't see what's unique about 接连 and 一连 but they seem different from the other two