I am typesetting a Bible right now and the current status is that each verse is it's own paragraph, so that there is a newline after each verse. I want to have them as freeflowing text, is it possible to have paragraphs on the same line in indesign?
You can run a Find/Replace from menu Edit → Find:
Find ^p
which is a paragraph end and replace it for a space .
Danielillo's answer is correct, but be advised in InDesign you cannot have multiple paragraphs on the same line. Default InDesign logic says every paragraph ends with a ¶ character and this is important because it also affects the way Paragraph Styles are applied in the formatting stage.
You can hit Ctrl+Alt+I to show these 'hidden' characters so you have a better view of where your paragraphs start and where they end.