Aside from embedding Podio Webform in your Website, you can also send form entries to Podio even you are using Wordpress form plugin by following these steps.
First, create an App in your Podio account
On your Project click Add App
Then choose Create your own app
Lastly, select Standard - the Podio default, useful for all types of apps
Then click on the Wedge icon, then Modify Template
Create text fields in your template similar with your form fields in Wordpress. Make sure that the labels for the text fields in your app is the same the the field label you used in the Message body in your Wordpress contact form. You can also add a Subject field for the Email subject. (See Screenshots 1 and 2 to compare ).
Get your Public Email by clicking on the Wedge Icon > Email to App > copy the Public Email address in the popup window. See Screenshot 3
Paste the Public email address to the To email address in your Contact Form Wordpress plugin (in my case Contact Form 7)
Finally, test if your Form is sending entries and is being sent to your Podio app.