Im creating a site using Joomla, and among the needs from the site is it uses the Phoca Gallery Component and Module. The issues with one of these is tthat there is a large amount of inline CSS styles, causing them to be difficult to personalize. I have solved this getting rid of the design and style characteristics with jQuery, however it does not appear like an excellent solution.

What could I actually do to resolve this issue?

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The only method to do that is to get it done correctly and obtain both hands dirty. Alter the inline styles and add classes to every html element which you'll later style via CSS. It is rather simple enough but time intensive, but when you need to personalize the appearance and steer clear of jQuery then this is one way forward.