"I like watching movies online."
I think that 上网 acts as an adverbial because it describes how the films are watched, and an adverbial usually goes before the verb it qualifies. Mandarin is more strict about the positioning of adverbials than English which basically puts them all over the place including at the end of the sentence as in this case.
It doesn't accept " wo xi huan kan shang wang dian ying" either though the positioning is as per what you say.
I don't think they've made it clear anywhere, but 上 sometimes acts like a verb or a verb phrase, meaning "to get onto" or "to mount". 网 is literally "net", so 上网 is really something like "to get onto the (internet)", i.e. "to go online", as opposed to simply an adverb or adjective ("online"). So you can say "I like to go online (and / in order to) watch movies", but not "I like to watch movies to go on line".
Well it seems to be acceptable...but I've never seen 在线上 is used to express "online" unless you are really standing on a line.
在线 and 线上 can both express "online", but they are used as adjectives.