So should I re-encode all my videos to OGG? I’m really confused what this means for the average person who has home videos encoded in these formats.

Note that OGG is not a video codec, it's just a container format. I.e. an OGG file can contain MPEG-4/H.264-encoded video.

Unless you're running a platform with millions of users, where you use the codec to encode/decode video for others, you have absolutely nothing to worry about due to these news.