总是 is just plainly always.
平常 is usually, as in being part of normal life. For example, 我平常有运动 would literally be "I do exercise as part of my life", interpreted as "I exercise often". If you want to say "Fast food is usually unhealthy", the usually would not be in the sense above, so 快餐平常都不健康 would be incorrect. Rather, that would have a weird meaning like "Fast food is unhealthy most of the time (but it is healthy today)".
通常 is also usually, but in the sense of being the more common/likely/normal/general case. For example, 叶子通常是绿色的 would literally be "Leaves are normally/generally green", and translates to "Leaves are usually green". The same fast food example would work for 通常: 快餐通常都不健康 would be "Fast food is usually unhealthy".
经常 means often. 我经常运动 would, like 我平常有运动, be interpreted as "I exercise often". However, the former directly states “I exercise often", while the latter states "I do exercise as part of my life", so note the difference.
An extra example, 我经常跌倒 means "I fall often", and the average person would not say 我平常跌倒 as it would be like "I usually fall". 我平常走路都会跌倒 "I would fall when I walk in the usual manner" would be more legit. 我走路通常会跌倒 would be "When I walk I usually fall".