As JAM already said, Russians prefer to hint at their feelings instead of describing them.
Instead of saying they're excited about new job, they'll say the job is friggin' awesome.
If you use words like возбужден
(which usually refers to sexual arousal for most people and atom state for physics geeks) to express your excitement you're risking to sound either too formal and insincere or too cute and funny, in case people are aware you're just a learner.
Instead, this is what I as native Russian would say if I was to communicate your sentences.
This is rather informal so Queen wouldn't approve but that's how people speak in their 20's and 30's.
I'm very excited about my new job.
To a friend
Кажется, я устроился в классное место.
(Seems like I landed an awesome job.)
To an acuqaintance
Я очень рад, что получил эту работу.
(I'm really glad I got this job.)
My trip to Europe was so exciting.
To a friend
В Европе было круто.
(It was cool in Europe.)
To an acquaintance
Поездка в Европу была потрясающей.
(The Europe trip was terrific.)
Are you excited about going to the party?
To a friend
Ты как, хочешь пойти?
(Hey, would you rather stay or go?)
To an acquaintance
Думаешь, будет хорошая вечеринка?
(Do you reckon it'll be a great party?)