If you're using Microsoft's Sway and you want to embed a Google Doc, there's just a couple easy steps to do it.

Sway with Google Doc
The title of your Sway

Create a new Sway and give it a title. I've called this one Embedding a Google Doc.

Media group
Choose the media group

Next, click the plus sign to add more content. Choose the Media group then click the Embed option.

Embed
Choose the embed option

Video explanation

Publish to the web
Publish your Doc to the web
Publish button
Click the publish button

Sway is now waiting for the embed code. You need to get the code from your Google Doc by going to the document's File menu and choosing Publish to the web. Once in the Publish to the web page, you need to click the blue Publish button one time to open up the Doc. After you have clicked Publish, you can highlight the embed code and copy it to your clipboard.

Embed code for Docs
Embed option in Google Docs

Go back to your Microsoft Sway. Go to the box waiting for your input, and paste the code.

Embed card with code
Sway card with embed code

You've embedded that Google Doc. This is live. If you were to update this in Docs, this document that's showing here would be updated. You can also interact with this document to a certain extent with the icon lower right hand corner. You can download it or print it.

Finished sway with Google Doc
Sway with embedded document