Creating a Character Style that defines the outline (stroke), then have your Paragraph Style auto-apply that Character Style to the entire paragraph via a GREP Style.
Select a word of the text that should have the outline.
Set the outline on that selection:
Swatches panel: set Stroke color.
Stroke panel: set Weight (e.g., 1–4 pt) and Join (Round/Bevel as needed).
(Optional) Set the Fill color in Swatches.
Open Window ▸ Styles ▸ Character Styles.
Click New Character Style (plus icon).
Name it, e.g., “Text Outline”, check Apply Style to Selection, then OK.
This captures the stroke color/weight and fill you just applied, so it can be reused.
Open Window ▸ Styles ▸ Paragraph Styles.
Create a New Paragraph Style, or right-click an existing one and choose Edit.
In Basic Character Formats, set your normal font family/size/leading.
Go to GREP Style (left pane) → click New GREP Style.
Apply Style: choose Text Outline (the Character Style you made).
To Text: type the pattern ^.+$
This targets all characters in the paragraph from start (^) to end ($).
Click OK.
Result: Any paragraph using this Paragraph Style will automatically apply the Text Outline character styling to all its text—one click, fully editable.
Select your text and click the Paragraph Style name.
All text in that paragraph gets the outline.
Change outline thickness/color later by editing Character Style → Text Outline once; all paragraphs update instantly.
If some text doesn’t change, clear local overrides: select the paragraph → in Paragraph Styles, click Clear Overrides (¶ with a slash).
For headings only, make a dedicated Paragraph Style (e.g., H1 – Outlined) using the same GREP Style rule.
For multi-line paragraphs, ^.+$ works line-by-line in InDesign’s GREP; if you ever see a blank line not styled, use .+ (no anchors) which also matches each line of the paragraph.