How can I prevent my house from smelling like the food I've cooked for hours afterwards? Often when I cook on the stove top, it will involve something fragrant like garlic, onions, seared meat, etc. I'm fine with smelling it while it cooks, but it seems to permeate the air and linger for hours afterwards. To make matters worse, my house has an open floor plan, so the smells spread to the living areas as well. 

I have tried running the vent fan, which is connected to the outside, but it doesn't seem to make any difference. It's also very noisy, so it's not pleasant to use. (Maybe something is wrong with it?) It gets cold here for every season except summer, so opening windows is not ideal. I clean up the dishes while or immediately after cooking, so it's not a dirty kitchen that's causing the smells.

What can I do to prevent these smells or get them to dissipate promptly? I own my home, so solutions that involve modifying or replacing something are fine.
When using a hood you need to think about where the fresh air comes in to replace the extracted air.  It has to come from somewhere. If the rest of the house is completely sealed the fan will be useless.

Opening ventilation close to the source of the smell can mean that air is drawn from the inlet to the hood bypassing the cooking.  So what I find most effective is to leave open the trickle vents over the windows in the living room, and close the ones in the kitchen (not exactly open plan but open double doors in between).  Leave the fan on from when you start cooking until after the heat is turned off, by which time most foods will be covered, and the waste dealt with.

Cleaning or replacing (as appropriate) the filters in your cooker hood can improve airflow quite a bit and may even reduce the noise.  Unfortunately they usually are noisy, but mainly for the cook.  In an open plan house that's an issue because you probably want to hear your guests.