Translation:This building is lower than that tower.
„Do” has completely different meaning. Simply speaking it means "to/towards".
„Niż”, beside being also a meteorologic term, is used like English "than" in comparisons like the one above.
„Od/ode” is basically "from", but it is interchangeable with „niż” in these kinds of comparisons. The use of „od” or „ode” depends on the following word. Basically, if the resulting cluster would be too difficult with „od”, we use „ode” instead. It behaves exactly like „w/we” or „z/ze”.
EDIT: Clarification: After a quick query I only found two relevant uses of „ode”.
One is „ode mnie”. The other is in Lord's Prayer: „ode złego” (standard modern Polish would say „od złego” instead).
I've just come back around to this question having (I think) learned something since the last time I was here.
"Od" does indeed take genetive, whereas "niż" does not affect the case (i.e it does not "need nominative").
So in this sentence "tamta wieża" remains in nominative, but if another case was required it would remain in that case.
For example: Lubię ten budynek bardziej niż tamtę wieżę.
Please don't take too much notice of this until some competent person has confirmed/corrected it. ;)