How do I say this correctly and naturally? Thank you.

Most of these are pretty complex sentences, so there will be a number of ways to convey the idea while sounding natural, depending on what words you like best.

(Food, pharmeceutical, bread, etc.) Products have expiration dates.

This needs some sort of qualifier.  Not ALL products have expiration dates.  Whether it's a very general category or a specific type, without some sort of descriptor for "products," this will strike people as being too inclusive, or just incorrect.

The contents could develop a change in colour and/or odor over time even if they didn't pass prior to passing the expiration dates.

I think there is a little context missing here.  If you're refering to something that is quantifiable, such as the contents of a package, then you'll need that "s."  Is this refering to a specific type of product?  Could color or odor change individually?  There is something odd sounding about "didn't pass." 
 
The more recently a product is was manufactured, the further away the expiration date is from the present.

This is a very "matter of fact" sentence.  I feel like this is a sentence I might hear in a training video if I'm working at a grocery store or food processing plant.  I think there are a handful of ways to say this depending on your venue and your audience.

If a product that was made today had three year's' time to/until expire expiration, the expiration date for that product would be 6/6/2017.

Saying "X time to expire," is similar to, "You have one hour to finish."  It makes it sound like the product could expire earlier, but has to expire by the end of three years.  

If there are two products that are made within 6 months gap of term, one after another of each other, then the more recent/newer product has will have a futher back later expiration date.

I hope this helps.  : D

How do I say this correctly and naturally? Thank you.

Products have expiration dates.

I don't know the context of this sentence so to me I think it would be better if you described the products. For example, "Dairy products have expiration dates." or "Cleaning products have expiration dates." Whatever you are discussing, I would include that in the sentence.

The content could develop a change in colour and odor over time even if they didn't pass expiration dates.

"The product could develop a change in color and/or odor despite not having passed the expiration date."

The more recently a product is manufactured, the further away the expiration date is from the present. 

This sentence sounds awkard, I would say "The expiration date depends on the date the product was manufactured, an older product will have a sooner expiration date than a newer product." 

If a product that was made today had three year's time to expire, the expiration date for that product would be 6/6/2017.

"The product lasts three years before it will expire. If the product was made today, the expiration date would be June 6th, 2017." 

If there are two products that are made within 6 months gap of term, one after another, the latest product has a futher back expiration date.

"If two products were made 6 months apart from each other, the first product would expire sooner."

Or, "If two products were made 6 months apart from each other, the second product would expire after the first."

How do I say this correctly and naturally? Thank you.

Products have expiration dates.

The content could develop a change in colour and odor over time even if they didn't pass expiration dates.

The product could develop a change in colour and odor over time even if it has not passed its expiration date.

The more recently a product is manufactured, the further away the expiration date is from the present.

More recently manufactured products will have later expiration dates.

If a product that was made today had three year's time to expire, the expiration date for that product would be 6/6/2017.

If a product made today were to expire in three years, the expiration date for that product should be 6/6/2017.

If there are two products that are made within 6 months gap of term, one after another, the latest product has a futher back expiration date.

If two products were made six months from each other, the more recently manufactured product should have a later expiration date.