hen na hanashi desu kedo

I often hear this phrase. What does it really mean and how do can I use it?

Thanks

"It's ironic but honestly ~/speaking truthfully~/in fact,~"

"I know it's odd for me to say, but..."

Thanks for the two answers so far! But could anyone write an example sentence or situation in Japanese?

This sentence is just from a Google search.

"Hen na hanashi desu kedo, koushuu-toire ni hairu to, dono ichi no benki o tukai masuka?" (I know this is an odd question, but when you go into a public toilet, which pot do you usually use?)

Henna hanashi, Daitouryou nante darega yattemo onajida.
"I'm altogether too outspoken, but anybody who will be the President will go same way."

henna hanashi, watashi datte daitoukyou ni nareru.
"I know that i forget my place to say, but i could be President, too."

Henna hanashi, watashi to tukiawanai/tukiaimasennka?
"I know that I shouldn't say/it's wrong situation to say, but Will you be my girlfriend/boyfriend ?"

Thanks for the examples but I can read kanji so that might be easier for me, I hate romaji! hahaha

変な話ですけど、公衆トイレに入ると、どの位置の便器を使いますか？