I am not a lawyer, this is not legal advice, free legal advice is always worth what you paid for it
Yes, is the short answer.
in oklahoma the permits are issued by the Oklahoma State Bureau of Investigation, their website states they recognize all out of state licenses and since the open carry law simply removed the "concealed" language from the bill yes you can OC in OK
Louisiana. If open carry is legal in Louisiana without a permit then you should be perfectly able to carry without a permit in Louisiana, unless LA law specifically says a non-resident can't carry. you are subject to the law of the state you're in. if OC is legal in LA because there is no law that makes it illegal then yes you can carry with no permit, I didn't actually look up Louisiana law, so that's just to guide you in the right direction.
I've did some reading for you, according to the Louisiana State Police, your Texas CHL is honored in LA for Concealed Carry
Also here is Louisiana law as far as "illegal carrying of weapons" (RS 14.95)
It appears that open carry is not specifically regulated, the law says "concealement" which to me means that "openly" is ok, however in my state (Washington) we follow british legal tradition, which includes that anything not mentioned to be a crime is not a crime, I know the Louisiana follows French legal tradition to some degree, so I can't tell you whether anything is or is not ok or what not by myself, please do your own homework and verify this. "EMNofSeattle" cannot represent you in court. I'm just telling you how I see this.§95. Illegal carrying of weapons
A. Illegal carrying of weapons is:
(1) The intentional concealment of any firearm, or other instrumentality customarily used or intended for probable use as a dangerous weapon, on one's person; or
(2) The ownership, possession, custody or use of any firearm, or other instrumentality customarily used as a dangerous weapon, at any time by an enemy alien; or
(3) The ownership, possession, custody or use of any tools, or dynamite, or nitroglycerine, or explosives, or other instrumentality customarily used by thieves or burglars at any time by any person with the intent to commit a crime; or
(4)(a) The manufacture, ownership, possession, custody or use of any switchblade knife, spring knife or other knife or similar instrument having a blade which may be automatically unfolded or extended from a handle by the manipulation of a button, switch, latch or similar contrivance located on the handle.