This is how I would deal with the situations.
Younger DS - move the computer into the family/living room. Tell him he can have one hour of gaming after school work on an evening. Position the computer so that it is in full view of the whole room.
Change the settings for the computer and put a password on so that you have to sign in to allow him access, do the same with the Internet.
When you are not home remove the access completely.
Tell him if he wants more than 1 hours access that he needs to get a weekend job, a paper round or washing neighbours cars for instance and pay for the access, work out the cost electricity/Internet usage and make him pay upfront for computer time in 10 minute slots, like an Internet cafe.
If he is rude, obnoxious or refuses to do school work take 10 minutes off the hour of access until he changes his attitude, if he doesnt he loses the whole hour.
It will be difficult at first and he will resist it, but stay strong, eventually he will learn that it is this way or no way.
As for your older DS - You need to stop letting him walk all over you. Paying for him to go visit his girlfriend when he is refusing jobs that are 'below him' is completely unacceptable, you need to stop letting him treat you like his own personal cash machine.
You can't afford to pay his rent, don't pay it! Most students have no help, he needs to learn that.
So his flat mate will get kicked out, how is that your responsibility?
And your DS won't have anywhere to live in September, he can find accommodation at the same time as everyone else.
Why can't he live in the student house now and get a job there?
If your DS is a grown adult, he needs to learn to support himself.
Stop bailing him out, or you will be doing it for the rest of your life.
Tell him that when he gets back from visiting his girlfriend things are changing, he IS getting a job and you are no longer paying his rent or giving him any money, if he doesn't like it then he should not bother coming home.
While he is away/or before he goes find five jobs, take CVs into places and apply for jobs on his behalf, explain to them that your DS is returning from where he is at uni in a week and urgently needs a job.
Then offer him those jobs, tell him if he doesn't want one he can stay at uni and find a job there, as you are no longer supporting him.
And if he is receiving his inheritance that is even more reason for you to cut him off, If he is spending it on fun and games while you are paying his rent he really does need a shock back to reality.
If he doesn't learn some financial responsibility soon he never will, and you will end up supporting him and bailing him out for the rest if your life.
I know it is going to be hard, and you are going to have to deal with a hell of a lot of attitude and drama from them both, but if you don't fight the tide you will never make it to shore, and if you stay where you are you will probably sink and drown, as my mother always says.
Good luck, and remember MN is always here for reassurance and support.