I just recently moved into an old apartment. And I have noticed some strange things like a door opening and closing. My front room shakes every night I can feel it when I am sitting on the sofa and I can see furniture shake. My daughter has also seen and felt this.
My cats also seem tobe acting different and crying a lot. Someone told that it was most likely just the house settling but I don't think that is the case.

No, homes don't settle like that. However, if there is a train in the area it can certainly do that to a home. Some homes, while appearing level, can be off just enough to make doors move. These are just examples and ideas of course to give a non spiritual explanation. You live there and know the degree to which these things are happening. But of course there is a very real spiritual world out there and this can be your cause as well. But, being in an apartment, I might ask some of the other tenants if they either know what this could be or if they too have experienced these things. Let us know what you find out and we'll go from there.