Trying to answer your question but not quite certain what you want to know. I'll give it a shot but ...
"is the HDMI port on Mobos from a onboard video card ..."
Yes, The HDMI output on the motherboard creates its output from the built in video subsystem that is built in to the motherboard chipset or the CPU.
"...or it takes the video from the cards..." This sounds like you're asking if the video information can be generated by a discrete video card and then passed back to the motherboard video for output to the display. No, the motherboard can only create video from its own subsystem.
"...and the audio from the onboard audio card then mix them together on the HDMI output?" This sounds like your asking if the output from the Onboard Audio system is connected to the output pins on the HDMI output. Short Answer, NO.
The Onboard Audio system converts the digital data file stored on your hard disk to a digital data stream and then converts the data stream to an analog signal that is then sent out to the speaker system to be played in real time through the speaker outputs.
On the other hand the HDMI output on the board sends a digital data stream to the display that includes both video and audio information. It is up to the display to decode the data stream and convert it to images on the display and sound through its speakers (if it has speakers).
Since, HDMI (as well as DVI and Displayport) uses digital data, a separate device is required to mix in the audio information. This is usually called an "HD Audio Device" or something similar by the system and it is included as part of the digital display interface.
If you use a discrete graphics card to drive the display then it has it's own digital display interface which is separate from the one on the motherboard and also includes its own "HD Audio Device". Therefore, it also has HDMI, DVI, Displayport, and/or VGA Dsub outputs(may have many combinations including missing certain ones).
I hope this answers your question(s).