The real problem here is that the IT company takes days to months for things you could fix in the moment.
As such, I don't think the IT company is really doing its job properly (it might be more complex for them, but taking months for something apparently simple??).
Now, the IT company may be given more work than it can handle from you, they may be doing work for other companies that makes their response times for your employees bad, the contracted service may have been lower than what your company actually needed, they could have assigned people without the required expertise to work for your company, they could simply be incompetents.
The fact is, that your company has contracted another one to provide a service that "isn't really working".
If you do their job, you would be doing what they are payed to do, and it would simply hide the problem (whereas the IT company would still be payed in full, probably).
It could nonetheless make sense to do that, as it may provide more benefit for the company that you spent 5 minutes on problem X (company loses 5 minutes of your time) than being blocked for a month (coworker loses many more hours) waiting for the IT company, even if the IT company was to be payed anyway. However, in this case you have been explicitly told not to.
What your coworkers need to do is to complain to their manager that they have been waiting for N days for the IT company to do X, so they can't proceed with (they might even add "and Daniel used to do that in 5 minutes")
Then their manager would handle it properly, which could go from informing their manager about that, treating directly with the IT company, getting your manager to approve that you did this... (or, perhaps, do nothing and let X wait for months if it's not important or they want to see how it actually takes them)
By solving the problem, your bosses may think that everything is handled by the IT company while they actually do very little. Escalating the problem is the proper approach so that higher-ups are aware of issues caused by the high turn-around of the IT company, so that solutions can be taken.
Given that you were explicitly instructed to derive them to the IT company, maybe it was done so that you (and other Daniels there) could actually focus on your assigned tasks.
It is possible that -after being aware of the real extent of the issues of your coworkers that aren't being solved by the IT company- your managers find some intermediate solution, such as assigning you a couple of hours on Fridays to help your coworkers with the withstanding tasks that have been open for more than k days, but it is their call.
On the interpersonal part, simply saying "call the IT company" gives a message that "I don't care about your issues, I don't want to help, it's not my problem".
I think you should stop, look to them if you were not, showing with your body language that your are paying attention to them, and explaining them that you would love to help them but your manager doesn't allow you to (although you would happily help if allowed), and all these previous things I have been elaborating above. Let them rant about the terrible service of the IT company, they are not expecting that you are able to make them do a proper job, they are just sharing their problems (which will make them good, too), a response that simply expressed your sympathy would be fine.
Yes, it may take more time than fixing their petty issue, but I think it's the right approach here. Maintaining a good workplace environment is well-worth dedicating a few minutes for that (and you are spending them by following your manager orders of sending them to the IT company, anyway). Of course, you don't need to repeat everything to that coworker to which you have already explained it everything multiple times yet continues going to you.
PS: I hope your company has this properly set up, so all these tasks go through a ticketing system, which would provide the data for the actual turnaround, time spent, etc. Maybe it only took them a month once, and it was for a task actually hard, or there where other tasks with much higher priority going on at that point. It could be that tasks take a long time to solve, but there are actually things that the IT company needs from your company (from authorization to do Y, to clarification from the requestor what they really need) that makes it slow. A good system like that would allow to find out where the issue is and, if it is really their fault, provide evidence to demand they improve their services, or replace them with a better one.