So many intranet sites only work in IEWatch
Why is this?
Some of the intranet sites just load lots of popups and the layout is funny in Chrome
If using Chrome prevents you from being able to do your job, then you need to raise this issue immediately with your boss, and let her/him know what the issue is (e.g. show them a page which you need that isn't working properly).
On the other hand, if they've asked you not to use Internet Explorer, and the only problem is that the pages don't look quite right, but are otherwise entirely usable, then by all means you can still raise this with them, but also be prepared for them to tell you that the appearance of the page isn't important as long as it works properly.
From a technical point of view, Internet explorer supports a bunch of non-standard features which aren't portable to other browsers. It sounds to me like your company's intranet is probably an old site which might pre-date some modern web standards. Historically, some companies used to use features in Internet Explorer which weren't available in other browsers (back in the mid 2000s, this was deemed acceptable because over 90% of users on the internet were using Internet Explorer - back in the old days before smartphones existed when nearly everybody used Windows XP to access the internet). This is is why websites designed for MSIE will sometimes look wrong in Chrome/Safari/etc.
Just remember, as an employee of your company, the terms of your employment will almost certainly mean that you're responsible for complying with any requests they make like this, even if they seem strange or inexplicable to you. The best thing you can do is make them aware of the problem, and you could politely ask them whether they would be able to explain to you what the problem with internet explorer is (e.g. perhaps there are security concerns with Internet Explorer, or maybe the intranet site is unreliable with Internet Explorer, and it might be known to cause technical issues with the back-end systems - Again, if it's an old, poorly designed, poorly maintained system, then it is entirely possible that they've found a "bug" in their system which means it breaks with Internet Explorer..).