Should I decline unrelated work assigned by PhD advisor?

Very politely notify them your scholarship and RA position (or whatever it is called that requires you to do work in return for money) has ended, and offer a consulting rate to continue. Make sure there's an agreed-upon number of hours for each task, so they aren't thinking they can give you one hour of work at a time, when the emails alone take longer than that. Research in most fields doesn't happen unless there is a fountain of money behind it, so this is not as beyond the pale as it may seem from your perspective. Just be careful to make clear it is simply the economic situation of the real world (which apparently they forgot they live in) that is the issue, not that you are making these demands to be unhelpful and make them go away.

If they can't pay you, then you can offer to help someone else take over the work, for example by giving them a list of steps and answering their questions via email.

Or you can offer to help in exchange for co-authorship, but then make sure you get into the loop so it is clear to all that they are violating journal terms by not including you as a co-author. If they are dependent on your analysis for their paper at this point, they may put in a position where you are compelled by professionalism to help them finish, but of course this needs to be out in the open with a promise of at least co-authorship in return.

Everyone with valuable skills has to deal with this kind of thing. People will push until you push back. The overwhelming majority aren't necessarily as cutthroat as the occasional bad joke might imply; they just convinced themselves your time is near-worthless while theirs is precious. Clarify to them this is not the case anymore.

Just to clarify, when you say "holding their recommendation letters hostage", do you mean that that other group would refuse to provide you a recommendation letter, or that your advisor would refuse to write you one, if you didn't do the required work?

My first advice would be to talk to your advisor, especially since your scholarship has run its course. No reasonable person would insist under the circumstances, but you should also consider that there might a misunderstanding, e.g. that your advisor feels that you benefit from such an arrangement, so an honest conversation might clear everything up. However, if the latter part of my question is the case, that goes beyond unethical and I wouldn't be surprised if your problems wouldn't matter to a person like this.

There are a few options you have. First, is to unconditionally refuse to do the assigned work and take the consequences, whatever they might be. Second, to conditionally refuse to work, i.e. you won't do it unless they compensate you for it (pay, authorship, etc.). Third, to suck it up, as you are about to graduate soon and hopefully leave that institution, it might be worth considering that this is the last time you have to do something like that.

Now, what worries me the most is the possibility that your graduation could be sidelined or delayed in order to force you to work more for them (you didn't comment whether or not that was a possibility). If that is the case, all the other options are rather useless and in comes the fourth option, that I deliberately avoided above as being the most destructive: escalate the whole thing to the higher-ups (the department level, the university level, maybe even an attorney) and hope that in some future your case will be resolved.

Based on the question, I can't gauge the scope of the corruption, i.e. is only the advisor corrupted, does the other group know that you are essentially forced to work for them, for free, does the department condone such behavior? That and the location your based at, should help you define the impact of the fourth option.

Bottom line, my advice is: get out of there as soon as you can. Make a cost-benefit analysis of your next actions. Ask yourself questions like: What would it take just to graduate? What would it take to graduate and ensure reasonable recommendations? Can I afford it (and here I don't mean just the financial part, but also the price in time, mental health, opportunities, etc.)?