Note: Unfortunately Wordpress prohibits embedding of most 3rd party content including Omny Studio embeds on their free tier of a hosted wordpress.com site.
You can embed Omny Studio widgets into your Wordpress site by first copying and pasting the embed code for either a clip or a playlist. To find the code, click on your playlist, click on the playlist, head to the "Details" tab and then select "</> Embed".
Choose which style of widget you want, and then click on "Copy to Clipboard" to copy the embed code.
When creating your new page or post in Wordpress, go into the "text" mode and paste the embed code. Click "Preview" to see what the widget is going to look like on your site before hitting Publish.
For more detailed Wordpress support, head over to https://wordpress.org/support/.