Trishytee - take a look at this on-line depth of field calculator:
dofmaster.com.
Pop in some of the focal lengths and apertures you have used in your own images and take a guess at the distances to your subjects. You will soon see that depth of field on long focal length lenses is next to nothing. Combine trying to avoid camera shake with moving subjects and you can some appreciate that those who post good bird images are highly skilled at their art. But they only got that way from practice and learning about their equipment. The beauty of digital is that learning is cheap (no rolls upon rolls of disappointing images to pay for).
In your second image (340mm at F6.3), if I were to guess you were 5 metres from the birds, the depth of field (the range of acceptable sharpness) is 2.4 cms in front and 2.4cms behind the point of focus. And the drop-off from there to semi-abstract bokeh is very fast. The good news is that you did a great job of nailing the focus on the mother bird. The narrow depth of field has made her stand out as the primary item of interest in this shot, which is well deserved in this case with such a good catch of dragonflies.
I have gone so far as to install a depth of field app on my mobile phone, so I can check what DOF I might be dealing with while out in the field (even if out of mobile reception).