I need to find the value of each vowel. All vowels are worth the same amount in each work but each vowel has a different value: Audacious=$260, Equivocation=$340, Inimitable=$255, Onomatopoeia=$435, Unambiguous=$255?

You have 5 equations in five unknowns. For example, from the first word you have

2a + 0e + 1i + 1o + 2u = 260

Solve in the usual way. Here's a hint to get you started: note that "audacious" and "unambiguous" have the same number of each vowel except for one less 'a' and one additional 'u' in "unambiguous." Hence you know that 'u' is worth 5 less than 'a.' So you can substitue a+5 for each occurrence of u in the first 4 equations. Now you're down to 4 equations in 4 unknowns. By the way, when you solve this you'll foind that some letters are actually worth negative points.