Maybe 我今天吃过午饭了or 我吃过午饭了 is common, because we usually talk about lunch in the afternoon. Besides, we often talk about dinner they will take or they have taken today, so 今天 is removed from the setence. Sometimes people talk about the dinner they taken yesterday, but the dialogue may be : 你昨天和谁一起吃的午饭？你昨天午饭吃什么啦？你昨天在哪吃的午饭？ 我昨天在家吃的午饭...

我今天吃过午饭了。Personally, it's the most common way to say that. 我今天吃了午饭 is sightly different in that you can say the same thing about what other things you've done, the point is you're only making a list of what you did, instead of emphasizing on that you've had lunch (to refuse an invitation to lunch and stuff) like the first sentence. e.g. 我今天吃了午饭，看了电影，还去爬了山。

I have eaten : means you have done this action . <~~~~~> 過 = have done (one activity ) already . For your 1 and 2: 我今天吃 ： I do one activity : eat. May be today You already did a lot of activities. While, EATING just one of them. In 1 and 2 , you did not mention : " have done (something ).

上面三个句子，都可以用，在口语中完全能相互替换，不用区别！~