Oops, according to the dictionary, it is better to translate 立春は暦の上での春です。 to Risshun is the spring according to the almanac (or calendar year). So here it means "according to".

日本の会社で働く上で、注意しなければならないことは何でしょうか。 (In order) to work for a Japanese company, what are the things that you need to be careful or pay attention to? So here, "In order to" or just "to". 法律の上では平等でも、現実には不平等なことがある。 (Legally or) In term of law, they may be equal but in reality, they may not be equel. So here, "in term of" is a good trasnslation. 酒の上でも、行ってはいけないことがある。 There are things you cannot do even under the influence of Sake (or alcohol). Here, "under the influence of". 立春は暦の上での春です。 Risshun is the spring in (term of) the almanac (or calendar year). Here it can be "in term of" or just "in". So the meaning varies slightly depending on the context but generally "in", "in term of" or "in order to", etc. Note that 上(ue)　literally means "above" or "on top of" or "over". I hope this helps.