Hi. I can't explain 26 meanings :-) But I can tell you that there are ３ Kanji used. I think you can look it up in the dictionary for details. 上げる = generally means to make something higher, lift up 挙げる = e.g. 例を挙げる（give examples), 祝杯を挙げる（to celebrate) (this one, perhaps you should just memorize examples as so many ways to translate, depending on the context). 揚げる = to fry, or to bring a flag high, etc. When there is no fitting Kanji it means "to give". e.g. 本を君にあげる。（I give you a book). Also it can be added to a verb to give the meaning "this is done as a favour". So 日本語を教える。（I teach Japanese) 日本語を教えてあげる。（I teach Japanese as a favour (for someone) or volunteer. So it also implies that the first sentence, the person may be paid to do so; but the second one is generally not paid (or paid less than normal).