it doesn't look overcast in the photo - there are potentially two things that may have happened. (in fact i actually think it's a combination of the two)
1) you did have the polariser on (my guess, based upon the colours in the image and the exposure details). i'm hoping the polariser you have is a circular one. this allows you to turn the polarised 'grate' to allow the light's waves to come through in one direction. ideally, you turn the polariser so this happens at right angles to the sun. as you look through the viewfinder and rotate the polariser, you will actually see the colour of the sky change from a very nice dark blue to a dull paleish blue. try this next time you take the shots and try to take it with the darker blue sky (or better yet take it both ways so you can see the difference. one problem with polarisers is the affect they have on other colours, depending on the type of material (how they reflect light). also different polarisers have different 'tints' to them as well (depending on things including the coatings) - like when you wear polarised sunnies. in fact if you have polarised sunnies, you can see the affects on the sky, clouds, cars, car windows, trees, etc. by merely tilting your head from side to side. this won't matter on non-polarised glasses. fwiw i generally only use a polariser if i'm shooting a landscape because they can add an additional and often unmanageable colour element to the image. this can be really bad if your subject is a person. you will also lose some light (another reason i'm guessing you had your polariser - iso 400 @ 1/250 f7ish in daylight). i do sometimes use two polarisers like a neutral density filter (i have 2 b+w 77mm CPLs because i have so many 77mm lenses).
2) the sky is very bright and the blue colour tends to get lost due to its intensity and how sensors work. this is compounded by the 400 iso setting and possibly a lot of light cloud cover (not overcast, but 'misty' clouds). on my last trip to both DisneySea and HK
Disneyland, i was bummed that the sky was overcast in tokyo and hazy in hk. generally, the best day is nice blue with some puffy white clouds - to get good exposures and give good colour to the sky. if the sky is bright, underexpose a bit to save the colour. use the histogram to check the exposure, or bracket to be sure if it's a shot you really want to capture.
what can you do? there are a few things for next time, as well as some things you can do post processing now.
-you mentioned that your kodak easy share just takes great pictures. you can actually set your XT to behave more like this *if desired*. in the menu, there should be a setting which you specify which image 'set parameters' you're using. it should say something like 'set 1', 'set 2', and 'setup'. if you go into this setting, you can increase the saturation a notch or two to get more colour. the downside to this is you're permanently modifying your images. they'll look a bit nicer out of the camera, but you run the risk of being too saturated or the colours being wrong. Canon sensors tend to be overly red sensitive. i shoot with saturation on '0' and sharpness on '-2' because i do everything in post.
-shoot raw. you have far more control over the exposure, saturation, white balance (for example, just because you're in the sun doesn't mean the light was 6500k). obviously you will need more time to process your images so doing so means establishing a workflow process.
-fix the image using software. i'm not a big photoshop user - there are some very talented PS users on this board who can run circles around me so i'll defer to them. but there are times when it proves its worth, so i'm glad i have it. in the case of the images above, it would be very easy to fix the sky in PS, PS elements, Paint Shop Pro, and even GIMP.
i highly recommend trying some or all of the ideas above before your next adventure. go out and spend an afternoon shooting around the neighborhood with the polariser (so you get a good understanding what it will and won't do), with the saturation up, and raw. and then spend some time with your software playing around with the results.
oh, and btw for people who have very fairly wide angle lenses - you can orient the polariser properly (so the sky is nice and dark) but you can see banding in the sky. this is due to how the light is hitting the sensor directly perpendicular to the sensor in the middle of the image compared at an angle on the sides.
i'm sure i left something out but my daughter is asking me to read a story so i'll fix it later if i forgot (or messed up)