Hello, I liked your story and I think you have a pretty good understanding of tenses, but seemed to confuse them in trying to express your story without repeating the same phrases.  Don't worry about that, and just tell your story.  In English, sometime what seem redundant is actually what helps bring emphasis of key points to your story.

Reject an invitation.

Last week she invited me, however I ought to pass on her invitation. (This sentence is first missing the word "have" after "ought to" because it is talking about something that already happened, and the "ed" on "pass" because it, too is in reference to something that previously occurred.  So it should read "I ought to have passed".  Not only that, but normally we would say that we "should have passed" on the invitation.  I changed the sentence entirely because if you were to say that at the time that you accepted the invitation a week ago, you should have passed on it, it implies that you had knowledge of future events- i.e., you accepted the invitation even though you knew it would be raining badly when you were due to go the following week. Because I didn't think you meant that, I changed it.  If you did mean to say that, then you would have had to say : "When she invited me a week ago, I really should have said no because the forecast predicted it would rain that day/week, and it did/that is exactly what happened."

For starters- You cannot use this phrase unless you intend to list multiple points afterwards.  To say it was pouring and you forgot your umbrella is more like one point, seeing as the lack of umbrella simply supports the issue of pouring rain, and even if you had had one, you would have still have been uncomfortable and or wet.

During the journey I was ranting all time-Two things for this sentence: 1) to use the word journey implies a very long way.  Something like all day, several days or more.  We don'd typically use it if we are walking to a familiar and somewhat short distance.  2) ranting is very strong and implies almost a crazy, furious, over the top expression of anger.  Most likely not what you were doing.

 take down- "Take down" is used to express a literal action of removing something from a higher level and bringing it lower, or more metaphorically of putting words to paper.  You could have said "turned it down",  but in this case I would use the word "cancel", because, again, you didn't have prior knowledge of how bad the weather would be, therefore you could not "turn down" the offer, which you would have done at the time it was presented.  Instead, because you no longer wished to go do to the bad weather you only found out about the day you were due to visit her, you should have "canceled your plans."  Also, in this case you can not say cancel the invitation because that would imply that you are the one extending it.  You we given an invitation, and can therefore accept or reject (as you titled your entry) but after an acceptance it becomes a plan, date or appointment you then have to confirm or cancel. 

Reject an invitation.