OK. I'll try some of the suggestions. I wasn't sure about how high up on shutter I should go but I'll try it. Lens is just the kit lens at 250 mm. Looking for a better one but have budget concerns. As for the shadow on the head, that seems to depend on which way they fly and never seem to cooperate for me. These images were cropped about a third. Thanks for the input.
ok, 1/2000th sec is quite fast. I'd be looking to hit that speed or up to 1/2500th sec if the action was fast, like shaking or grabbing a fish out of the water. You could probably drop it a little if they are not in a dive, but at ISO 800 you are well within the parameters I'd consider accepable for good shots. Indeed I'd be happy to push it to ISO 1600 on your camera before I'd be starting to think about trading a little shutter speed. So I think your settings look good to me.
From the exif data you seem to be using an EF-S 55-250mm f4-5.6 IS STM. It looks like an ok lens to me, not the sharpest but not totally terrible. Most of the super sharp shots you'll see will be shot using the big primes, which are generally very sharp but costly. A lot of Canon shooters look towards the 100-400mm f4.5-5.6 L as good quality versitle lens. A few of us go for the 150-600mm superzooms from tamron and sigma, they tend to be slightly softer and the AF not as fast but the reach is great. So I'd probably place a little blame on your lens, being a little short and slightly soft but I would expect your shots to be a bit sharper.
Lenses are often not the sharpest wide open, so I'd stop down to f8 and see if that makes a difference.
Cropping by 1/3rd is getting towards the limit IME, but I'd expect that still to yeild acceptable shots.
How are you post processing? Noise reduction can destroy fine detail so I'm wondering if you are underexposing a bit, bringing the exposure up in post then reducing the noise too much? I've seen that before a few times.
The only other things I can thing of right now is if you are not getting the birds in the centre of the frame (lenses are at their worst at the edges) or if your AF settings are missing focus. I'd check your AF point(s) are actually on the bird and test your lens for back/front focusing.