For example, what is the difference between 減少（する） and 削減（する）? Would prefer an answer in English.
And also which one is more correct? この株価は３年前からずっと減少している or この株価は３年前からずっと削減している。
Also, are there other ways to say reduce or decrease?
減少する is usually used as an intransitive verb and means "get smaller in volume/number". For example, 日本の人口は、減少している (The population of Japan is getting smaller).
削減する is a transitive verb and means "cut", "reduce", "curtail". For example, 多くの会社は、人件費を削減したいにちがいない (Many companies must want to reduce labor cost).
下落 and 下がる are appropriate for prices, so この株価は３年前からずっと下落している is natural.
I believe that 減少 is used to denote something simply getting quantitatively smaller (like weight or money) while 削減 implies some getting-rid-of or cutting. In the sentence you gave the thing that is decreasing is a stock price, from which you can't really cut or remove, it just changes in size on its own so 減少 is probably more appropriate. If it were something like employees at a company being laid-off, perhaps 削減 would be better.