Hi Mary,
There are a couple of things that come to mind when photographing these birds. Firstly. carefully choose the weather or time of day when looking to photograph them. White birds generally photograph best on days with even soft light. So days with lots of small light clouds around (like you see at the start of the Simpsons) makes for favorable light, as will light overcast conditions. This sort of light will make the contrast in the picture manageable, and gives good modeling (the light will give a more three dimensional look to your picture).
You will be heavily reliant on the latitude of your camera. This is jargon for how well the camera can differentiate between blacks and whites. As you push the ISO's up on your camera, it looses its ability to "see" this. My camera at it's base ISO has 14 and half stops of latitude. As I double the camera's ISO, I lose a little over one stop of latitude. With a black and white bird, you want to preserve as much of the difference as possible, so you should try and choose the lowest ISO you can. Also check what profile setting of your camera. A setting like "vivid" or "scenic" should both be avoided. Stick to "normal", or better still, "neutral". The colourful settings increase contrast and colour at the expense of detail. The subtleties of the two birds you mention will be lost in the Kodachrome look these settings give you.
The White-winged wren is an extraordinary bird to see see. Depending upon where it and you are, relative to the sun, it can be either black or the most amazing blues. turquoises and violets. Since both birds you mention are quite nosy (aren't all birds?), set yourself up sun from the tallest object in the area. With White-wings, this is usually some box scrub just four or five feet of the ground. If they are in area area, they will come to check you out if you sit down low in the scrub. Some folk will use a flash. It does scare them if it's bright. Set to less than 2 stops it will give you the colours we were talking about, without you needing to worry about where the sun is. However, I've know the wrens to disappear straight after the first flash.
With the robin, they too like to pick the highest point around to check you out. So look for somewhere where they can take a look at you and you them.
Both birds will stay around for quite a while if you have set yourself up right. If you have used a bird call, they appear to get extremely angry - usually described by photographers as "singing up a storm", or they just hop it and are gone. I find the silent set up and wait method gives you pictures of birds that are curious and not upset. I'm often surprised by how little interest such pictures get, but that's my preference. We are all different.
Please let me know if I haven't been clear enough in my explanation and I'll try to improve it.
Good luck.
P.S. Both images were taken with a D300 ( that's a 12 meg camera which is now very outdated) using a 70 to 200mm lens, from quite a long way off. Don't try to get too near or you will just lose your bird.
And one last thought, I like to use a tripod. You can often set the shot up before hand and choose your background with more care than otherwise.