Tim Bowen explains why an English student could run into some problems trying to form phrasal verbs with the verb to run.
Up and down are clearly opposing concepts. When you use them as prepositions (and not as part of phrasal verbs), you can run up a hill and then run down it again. If only phrasal verbs were as simple!
You can run up a large bill in a restaurant (accumulate an extensive debt) or you can run up a pair of trousers (make them very quickly). However, if you run someone down (as in You’re always running me down), you criticize them unfairly and if you run down a business or a factory, you gradually allow it to become smaller until it eventually closes. Similarly run in (to) and run out (of) are not opposites as phrasal verbs. You run in a new car (drive it slowly so that you do not damage the engine) or you run into someone in the street (meet them unexpectedly), whereas if something runs out, you have no more of it left (as in They returned from South Africa when their money ran out). Also related to driving, if you drive into (usually at speed) and knock someone or something over, it can be said to have been run down ('the assassin ran the victim down with his truck). Similarly, if you run over something you drive over it and cause it injury ('Our cat got run over last week').
In the case of on and off, an event like a meeting can run on (continue for longer than expected or planned), but if you run something off, you quickly print a copy of it (Could you run off some copies of the agenda?) or you quickly compose something like a poem or a speech (James can run off a speech for any occasion). Finally, if you have been running around all day (very busy doing different things), you may not have time to run through (rehearse) that speech James wrote for you, which might cause you to run up against (encounter) a few problems.