I have a website that provides 42 search parameters. Of those 42 parameters 5 account for about 900K searches performed. The other 37 are used very rarely and account for about 21k searches combined. Is there a method to determine at what threshold I can safely eliminate those items to declutter the UI and order the more well used features?
Remove it, but test.
If the 37 parameters account for ≈2.333% of searches, they're averaging ≈0.063% each. But, queries vary by importance. As an example, if your users are searching Google for "hospitals nearby" it's likely a lot more important/urgent than "7 Eleven nearby," even though it probably accounts for fewer queries.
Discover the intent of users who want the additional parameters.
You may want to look into the Pareto Principle for decision-making. It states that "roughly 80% of the effects come from 20% of the causes." This article also provides a more UI-centric discussion of the same issue. Its key point is "if you leave features in your application just because half a dozen people actually use them, you’ll end up with Microsoft Word."
All that being said, attaching a wireframe/low-res mock/screenshot will allow the community to provide a better answer. Depending on the query UI (eg. toggles for parameters, structured queries à la Google's searches, etc.), the answer can differ dramatically.
My process for this particular issue would be as follows.
1) Determine the metrics you'd like to ultimately improve.
Saying "declutter the UI" is a design choice. Make it a UX choice by determining what exactly you'd like to gain by removing certain options. Do you want to see an overall decrease in the amount of time it takes to perform a search (task time)? Increase search volume? Really draw out what you're trying to accomplish beyond tidying the interface.
2) Testing via A/B
Design some new comps and test them accordingly. Use your metrics above to determine whether or not your changes are strong. If this is a critical task, involve moderated user testing to get more valuable information. Make iterative changes and re-test.
3) Deploy and monitor
After the process, continually check and make sure you're meeting the initial goals you set out for.
You can always do an axe test... http://zurb.com/apps/free-apps/axe
This will allow users to indicate which UI components are unneeded.
Usage data is directional. It tells you what is happening, but it doesn't tell you why something is happening. If you simply apply a metric for removing a feature, you could be doing your users and your application a huge disservice by removing it without having a full understanding. Likewise, decluttering is a noble goal. It's also important to understand whether your users think that your UI is cluttered, and whether this particular area is an area where decluttering is necessary.
Your step now is to understand why these features are on the long tail of usage. For example, the vast majority of the time, a simple text search meets my needs, but those times when I do need to do a search using regular expressions makes me very happy that it's available to me, and I would be a very unhappy user indeed if regex searches were removed.
You don't say this in your question, so I'm not sure whether the top-five types of searches are successful. Do users start with these search methods and then move on to other search methods if they're unsuccessful? If so, how frequently does that happen? Is there a way that you can make your users' first search a successful one?
What are the workflows that result in a user using one of the other search methods? Are the other search methods more likely to result in useful or valid results for the user? Can a user get to the information that they need using one of the top-five search methods instead of one of these long-tail search methods? Would users benefit from using other search methods instead of one of the top-five ones?
With both usage data as well as a better understanding of your users and what they want to accomplish, you can make an informed decision about what design changes you can make to your search. If you make a decision with only half of this information, you are losing an opportunity to improve your design in a way that will truly impact your users.