Schema.org combining different categories
Home page

The Microdata is fine. 

I don’t know if it’s possible with the design of your page, but typically you would link the name/logo (then you could omit the meta and you wouldn’t need alt content), so it could look like:

&lt;body itemscope itemtype="http://schema.org/Organization"&gt;
  &lt;a itemprop="url" href="http://www.example.com/"&gt;
    &lt;img itemprop="image" src="company-logo.jpg" alt="" /&gt; &lt;!-- empty alt because the 'name' already describes the link target --&gt;
    &lt;span itemprop="name"&gt;Organizaton&lt;/span&gt;
  &lt;/a&gt;
  &lt;p itemprop="description"&gt;short description on home page&lt;/p&gt;
&lt;/body&gt;


Product page


You are using the name property (from TravelAgency) on a meta element, but do you really have no visible name of the travel agency on your page (e.g., in the header)? If you have one, you could use that element instead of meta.
The itemOffered property expects a Product item as value, but you are using text. 

As you are already using Product → offers → Offer, there is no need for the reverse relation Offer → itemOffered → Product.

You probably want to use the name property instead, however, if the Product has the same name as the Offer, omit this property altogether.
If the only data about the Product is the name, consider omitting this item. You could use Offer directly (unless you have several offers for the same Product).
There is a superfluous &lt;/span&gt;.
Your span element has a content attribute, which is not allowed. Use a meta or data element (or in your specific case, just the content of the span.)