Japanese mini lesson 1 - Why is "おめ (ome)" a big deal?
Drama: You Should Be the One to Kiss Me (お前のほうからキスしてくれよ) - Episode 2

In ep1&ep2 when Ueno congratulates Kanda with an "おめ (ome)" , Kanda isn't really pleased haha. But why is that? Let's see how we congratulate someone in Japanese!

おめでとうございます (Omedetou gozaimasu) - Congratulations
(the u is not pronounced as a "u" in omedetou, it merges together with the o, making a long "o" sound.)
This is the full phrase. In Japan, saying the full phrase is super important when you want to be polite, just like ありがとうございます (Arigatou gozaimasu) (Thank you). If you've ever heard "happy birthday" in Japanese, you might have already recognised omedetou gozaimasu, as it's used in that phrase as well: 誕生日おめでとうございます。(Tanjoubi omedetou gozaimasu) - literally meaning "Congratulations on your birthday."

Now let's step down on the politeness ladder:
おめでとう (Omedetou) - Congrats
If we cut down the ございます (gozaimasu) we get the more casual version of おめでとう (omedetou). It's REALLY important that you shouldn't say this to people you are not friends with or to people who are older than you/ higher in status. The same goes with ありがとう (arigatou). E.g. It's considered to be rude if you simply say ありがとう (Arigatou) to a stranger, even if they are in the same age group as you.

And now we get to the word that Ueno said to Kanda:
おめ (Ome) - Grats
This is the most casual version of congraulations, like saying "grats". You should only use this if you are really really close friends. If not, it's considered really really rude.

So in Japanese usually the more characters = the more politeness and more respect you show toward the other person, which is REALLY really important in Japanese culture.
And Ueno only saying "ome" is
- on one hand, shows that they are really close
- but on other hand, is a bit rude too. :DD

P.s.: The last message "うざ" (uza), is the shortened version of うざい (uzai), which is the slangy version of the famous word うるさい (urusai). It's simply the adjective for "loud", but when they say it to someone, it basically means "shut up" or something like "you are annoying, stop" :D

That's all for now ^^ If you have any questions, feel free to ask!