Returning IHttpActionResult vs IEnumerable vs IQueryable

You should return IHttpActionResult because you can be more specific to the client. You can create more user friendly web applications. Basically you can return different HTML status messages for different situations.

For example:

public async Task<IHttpActionResult> GetMyItems()
{
    if(!authorized)
        return Unauthorized();
    if(myItems.Count == 0)
        return NotFound();
    //... code ..., var myItems = await ...
    return Ok(myItems);
}

IEnumerableand IQueryable will just parse your data into the output format and you will not have a proper way to handle exceptions. That is the most important difference.