tá léine oráiste orm is "there is an orange shirt on me"/"an orange shirt is on me" or, colloquially, "I have an orange shirt on". They all describe what is happening right now, and therefore they are equivalent to "I am wearing an orange shirt" (táim ag caitheamh léine oráiste), whereas "I wear an orange shirt" (caithim léine oráiste) is not describing what is happening right now ("I wear an orange shirt on Wednesdays").
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This is a late reply and I'm just a learner, but in case it helps someone: agam literally means "at me" and is what you would use if you just wanted to say "I have an orange shirt," literally, "An orange shirt is at me". Orm would indicate "on me" and is what you'd use to say, "I have an orange shirt on", literally "An orange shirt is on me." Please correct me if someone can explain it better.