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The sourness can be offset using a little sugar.  If you do not the flavor of vinegar, lemon juice can be substituted in equal amounts.  However, the reverse is not true --vinegar cannot be substituted for lemon juice when lemon juice is indicated in the recipe.

Here is plain tomato juice: http://www.uga.edu/nchfp/how/can_03/tomato_juice.html.  You can tinker with additions ---after--- you open it.

Here is the tomato vegetable juice blend: http://www.uga.edu/nchfp/how/can_03/tomato_veg_juice.html.  Note the recipes says, "Add no more than 3 cups of any combination of finely chopped celery, onions, carrots, and peppers for each 22 pounds of tomatoes."  This allows you flexibility to add the vegetables you like.

Without knowing the reasons you feel that the tomato-vegetable juice is not palatable, I cannot offer suggestions to help make it better.  If its sour, add a little sugar.  If one or more vegetables are disagreeable, use others as mentioned above.  You may be consuming it beyond its shelf life.  Most tomato products are good for one year and start to lose quality over the next year.  After two years they will definitely taste off.  If you are drinking it for health reasons and don’t like the flavor at all, there is little I can do to help.