I have written a program that uses several open source components. First off, it's written in python. Second, I use the modules subprocess, argparse, os and datetime. […] My goal is to disallow any use, modification or distribution of that program that is not explicitly allowed by our company. May I use a simple, standarized EULA for that?
Yes, you may do this. According to the Python Software Foundation License FAQ:
Can I bundle Python with my non-open-source application?
Yes. Unlike some open source licenses, the PSF License allows Python to be included in non-open applications, either in unmodified or modified form. See also this more detailed overview.
The only requirement is that you include some licensing and trademark related boilerplate text in your documentation:
If I bundle Python with my application, what do I need to include in my software and/or printed documentation?
You must retain all copyright notices found in the code you are redistributing and include a copy of the PSF License and all of the other licenses in the Python "license stack" with the software distribution. The "license stack" is a result of the history of Python's development as described here (this page also lists all licenses in the stack).
Separate from the issue of copyright, the name “Python” is also a trademark. You should include the notice “"Python" is a registered trademark of the Python Software Foundation” in the appropriate part of your documentation or About box and place the “®” symbol after the first mention of “Python” in your documentation. (For example: “Python® is used as the scripting language for...”)
And if yes, who's the Licenser? Me or my workplace?
Whoever owns the copyright to the code being licensed.
Usually, if you're working as a programmer and writing the code as part of your job, it should be fairly safe to assume that it's your employer, either because the code counts as work for hire under your local laws or because there's an explicit copyright transfer agreement included in your employment contract.
That said, weird edge cases do occasionally come up, e.g. in cases involving poorly written (or completely missing!) employment contracts, code written by people not primarily employed as programmers, or code that an employee has originally written for personal use in their free time and later used at work. And those cases can sometimes end up being really messy. If you're still not sure who owns the copyright to your code, all I can suggest is asking either the folks over at Law Stack Exchange or (for a more reliable answer) a local lawyer.
On a different note, would I be allowed to distribute the program if I left the company? My contract does not cover anything regarding code I've written during my time there.
If you, rather than your employer, really own the copyright to your code, and haven't signed an agreement transferring the copyright to your employer or granting them an exclusive license to it, then yes, you can do whatever you want with your code after (or even before!) leaving the company.
However, that would generally be a rather bad situation for your employer, since without a copyright transfer or a license, they wouldn't be legally allowed to use the code they paid you to write without asking you for permission. So, unless your employer seriously messed up, this is unlikely to actually be the case. Again, if you suspect that it might be, I'd recommend consulting a lawyer familiar with the relevant copyright and employment laws in your jurisdiction before trying to do anything your (former) employer might object to.
Note that, as I mentioned above, in some cases code written as part of your job might be considered "work for hire", with its copyright belonging to your employer, even in the absence of an explicit contract saying so. However, the conditions for this to apply vary a lot between different jurisdictions, so my suggestion to consult a local lawyer still applies.