How to Prevent Word Styles from Overriding InDesign Styles During Import

I wholeheartedly endorse Dave’s response here; it’s almost always faster to fix problems upstream. But it sounds like you might not be aware of the Customize Style Import tool, and I feel it’s faster to strip out miscreant styles here than it is to actually fix it upstream in Word. When you start your Place operation, there’s an “Import Options” checkbox in the file picker dialog. When that opens up, you’re given quite a few options regarding What To Do With Stuff In The Word Doc. At the very bottom of the dialog, you can choose to Import Styles Automatically or to Customize Style Import. If you choose to Customize, you can whack the Style Mapping button and choose which InDesign styles will be assigned to the spurious named styles in your Word doc. 

(In some cases, it might be faster for you to simply “Remove Styles and Formatting from Text and Tables” and reassign your styles in InDesign by hand, depending on the length and complexity of the target document.)

Try removing unwanted formatting in Word.

You can remove all character-level formatting and keep paragraph styles in Word by selecting all the text and pressing Cntl-spacebar. This WILL remove character styles too.

If you want to keep both the Word paragraph styles and character styles,

• make a copy of the file,
• open the Styles panel (Cntl-Alt-Shift-S), 
• click the Style Inspector button

• select all your text,
• click the Clear Character Formatting button