Indeed. "(On) Monday I have eaten strawberries" is very poor English. The completed time (on Monday) clashes with the continuing time (I have eaten). It sounds like something a German who has just started learning English might say. (No disrespect intended to German learners of English, by the way!)
DesertGlass, you'd use "Dw i wedi bwyta..." in the context of a time period that is still continuing. E.g. Y bore 'ma dw i wedi bwyta afal ac oren (This morning I've eaten an apple and an orange). As you suggest, if the time period were now over then you'd say "Bwytais i" (I ate): Neithiwr bwytais i oren a banana (Last night I ate an orange and a banana). Just like in English in fact!
Dydd Llun = Monday (as in "Monday is the first day of the week")
Ddydd Llun = On Monday (last Monday or next Monday, but -- in either case -- not today!)
Ar ddydd Llun = On Mondays / On a Monday (i.e, every Monday)
The literal meaning of Dw i wedi... is "I am after..."
Dw i wedi + [verbnoun] is the equivalent of the English present-perfect construction "I have* + [past participle],
Thus, Dw i wedi bwyta (lit. "I am after eating") = I have eaten.
And, yes, any time period referred to when using the construction must be an ongoing one: I've done it today (and I may yet do it again, because today's not yet over) versus I did it today (I'm looking back on the day that's now over).