Obligated means you have no choice. There could be reasons you are "obligated" to finish your work by the end of the day, but it sounds a little too strong. "I'm obligated to attend this boring work conference this weekend." sounds more appropriate because it's something you don't normally have to do and you really don't want to. Obligated has a very strong negative connotation. Obliged, on the other hand, can mean the same as obligated sometimes. However, it can also be a positive thing. In fact, where I'm from in the US, it's common to say, "Much obliged." instead of saying, "Thank you." To me, obliged is more often positive, and it means you are doing someone a favor.

"Obligated" is not negative unless you believe that the law is negative. An example of the use of "obligated" in the context of a contractual obligation: The actor Chow Yun-fat is obligated by contract to keep a beard for the next 9 months as he is playing a historical figure in the next movie.

See this definition of "obliged" when used as a way of saying thank you: "(be obliged) Be indebted or grateful: Example: if you can give me a few minutes of your time I’ll be much obliged" (from the Oxford Dictionary)

Neither sentence is correct! Just say "I have to finish all my work today." UNLESS it is a strict legal duty: you have signed a contract to that effect. "obligated" is strictly a legal or moral duty. "obliged" means the same plus it has other meanings which do not apply here. The temptation facing learners is often to use words they half understand. At the same time, they encounter a lot of bad writing. So it's not a fault to put this question forward. Niw you understand and will not use it.

"I am obliged to do something" is radically different from "I am obliged" as a way of saying thank you. They represent two different meanings of one word. It's the same word, but the two meanings are not to be confused.