I am non-EU family member married to a Romanian citizen. I am currently residing in Romania and I have temporary residence card here. As Romania is in EU but not in Schengen area, can we travel together visa-free within EU and Schengen countries ?
You can travel visa-free only if you have a "residence card of a family member of a union citizen" issued under article 10 of the free movement directive (or if you are a citizen of a country whose nationals don't require visas in the Schengen area). A residence card issued by Romania to the spouse of a Romanian citizen is not necessarily an article 10 card.
If you do not have an article 10 card, EU countries other than Romania must issue you a visa free of charge and on the basis of an expedited procedure. The grounds for refusal of that visa are strictly limited.
These provisions are also dependent on your traveling with or joining your spouse. In case you are not, you'll need a regular Schengen visa.
As Relaxed pointed out in a comment, it appears that your concern stems in part from the fact that Romania is not yet a full participant in the Schengen agreement. These rules apply to all EU countries, not just Schengen countries, because they are based on the EU right of freedom of movement. Your situation in the Schengen area is therefore similar to that of someone married to a British or Irish citizen.
Your Romanian spouse can, of course, travel visa-free in the entire European Union.