Sorry I don't have time to build a working version of this, but hopefully the following will get you started.
You can use
meta_compare= in your query to narrow down your posts. So your query might start like this:
<?php $my_query = new WP_Query('category_name=events&posts_per_page=10&meta_key=_EventStartDate&meta_compare=>=&meta_value="2010-05-24 00:00:00"'); ?>
This narrows down the posts to only posts containing _EventStartDate as a postmeta key, with the value of that field being greater than the date
2010-05-24 00:00:00. Instead of using that example string, you would need to generate a variable in the format of that string representing today's date, like:
<?php $date_today = datei18n('Y-m-d H:i:s'); ?>
Then you would have to add another part of the query limiting the posts to those having and
_EventEndDate less than some date a week from today. As I write this, I become more convinced we should provide this functionality with the plugin some time in the future.
Constructing long query strings can be annoying, so you could always stick with your current query, and then add the filtering logic within your loop, only echoing events landing in the correct week.