OK, this may take some time but it could get you a bit of freedom.
Tell your parents that you want to get a job when you turn 16. Use several excuses like, "I want to save up for college," "To get a job in college it will help if I have some experience," "When I'm at college I'll be pretty far away, I'll need some savings to come back home during vacations," whatever you think will work.
This will look like a mature decision and show you're concerned with the future.
Once you get that, you will obviously need a phone to call them if something goes wrong while at work. Also if you have to take a bus or walk to work, do they really want you to lose your job because you couldn't call and tell your boss there was a traffic accident and you'll be ten minutes late? That would look horrible at a future interview.
Now if you can manage that, when you get the job you can ask to work the evening shift. It would be a waste of time to head home only to head back out immediately, when would you have time to eat or do your homework?
It would make much more sense to be with some friends, who your parents know, to do homework at the school or a nearby library, and to eat with them somewhere close to your job.
Once you get your foot in the door, keep gently pushing to widen it a bit more.
Now about the bedtime, get a note from your teachers stating that your homework is not being completed on time. After your parents demand to know why this is happening, explain that you sometimes need a bit more time to finish it, but having to go to bed at 9pm stops you from doing it.
Really hope this helps.
Edit
All right, some people brought up good points in the comments and I don't have room down there to respond, so lets go over them.
The phone:
Concerning using a landline at work, that is an option. Which is why I said that the cellphone could be used on the way to and from work. What if she gets stuck at the bus stop, or is held up for some reason, having a basic phone is a good idea.
And if she does lose her job because she was delayed and couldn't let her boss know, being fired is a black mark in future interviews. She can either not put it on the future college job resume in which case she's starting from scratch, or she has to go in with a potential employer knowing she got fired from a McJob. Neither one is a great option.
Honestly, my first thought at reading the problem was to tell Sasha to ask for a cheap flip phone, one that could only send basic text messages and couldn't go on the internet.
However, then I read this,
For example, whenever I ask my dad if I can have a phone, he laughs
in my face and says "Well there's the joke of the day!"
So that is obviously not an option.
This is all about getting a chance to start a discussion, rather than getting shot down before the discussion even begins. Maybe after she has a basic phone for a while, paid for with her own money and used responsibly, she can upgrade, but that has to wait until she is actually given a chance to show the responsibility.
Eroding Trust
So my scheme definitely has an ulterior motive, but I'd hardly call it a bad one or even a real secret.
Getting a job is a good way to learn responsibility, if it gives her a tiny bit of freedom that's a side benefit for her. At most it would be three or four hours a week between school and work to do things with her friends, like homework. She won't be going off to parties or wandering around bars at night.
The phone would help her parents check up on her while she is out.
The most secretive and rebellious part of my idea is Sasha trying to get her hours set up so that she has the free time.
Also I did say this would take time, it wouldn't be done all at once. First she has to convince her parents to let her get a job, which will be a few months to a year away, then when it appears likely she'll get one she can ask about the phone. It won't exactly be a big secret that she wants more responsibility and freedom, but it's hardly trying sneak around her parents back. If that would erode the parents trust, frankly there was no trust there to begin with.
And looking at what Sasha posted, her parents have zero trust in her anyways. If they lose a little more because she wasn't 100% open with her reasons for wanting a job, what will they do, send her to bed at 8pm?
I really hope Sasha tries Eriks method first and that it gets through to her parents. However if it doesn't work, than she has three choices, sit back and do nothing, which will most likely develop into resenting and even hating her parents (I've seen it happen all too often with overbearing parents of students I taught in the past), rebel and stop caring what her parents think (NOT a good option), or pushing gently but steadily for a bit more freedom.