I had an issue like this with a co-worker once. Problem for me, was that my actual title was "Administrative Assistant" ... so one of the sales guys (who happened to also be the guy making the most in sales), started giving me work to do "on the side", or "when there's a minute of free time", etc. In actuality, I was doing Project Coordinator work for the owner, and just didn't have a title to go along with my arms-length list of projects and other responsibilities.
I would suggest 2 things to fix it:
First, mention it casually to the Office Manager.
Find the woman in your area who is kind of the "mother hen" type - the one who has the ear of someone around the same seniority as your VP (bonus points if it IS your VP) - and find a way to mention it to her. If you see her in the lunchroom, find a way to be near her and ask how it's going; ask what she's working on; ask other work questions to get her talking. It may take a couple of these Q&A moments, but when she asks what you're working on, tell her "oh XYZ project, but you know, a lot of little things for Steve lately too ... (laugh) ... sometimes I think I work on Steve's tasks more than my own projects!!" keep it as lighthearted-sounding as you possibly can.
She'll likely either express shock with "oh my goodness! Are you serious? What does he have you doing?", or will just respond by asking you point-blank what you're doing for Steve. I would mention at least 2 tasks that she would know are for someone else to do, like that travel budget. Just remember to keep it light, shrug your shoulders when she asks questions, and if she asks any sort of "why" question, just say "well I'm just not sure how to tell him no, to be honest ... I don't want to hurt his feelings".
Try your absolute best to keep any anger/bitterness out of your voice, and if she pushes for your opinion on it, just keep shrugging and "ah you know, it's alright I guess". You want to convey the sense that you aren't exactly happy about it, but you aren't spitting mad either, but you're just not sure how to deal with it. This conversation WILL make it back to someone who can change the situation.
So the Second option can be harder, especially because you sound as though you're trying to avoid any confrontation. The next time he comes over to assign you a task, tell him "oh, I'll have to ask (VP Name) about that. He's keeping me pretty busy. I'll clear it with him and let you know. Or hey, if you see him, maybe you can check that it's OK that I help you out".
This is doing 2 things: taking him to task over the shit he keeps throwing at you, so that he now knows that YOU know that you aren't supposed to be doing these tasks for him. And if he's really stupid enough to tell you to talk to the VP, or if he talks to the VP himself, then you don't feel like an asshole for telling him "no" - the VP will do that for you. And if he DOES say "yeah ask the VP", then you go to your VP and say "Steve came to me with XYZ task, and wants it done by XYZ date - my first instinct was to tell him 'no' because of XYZ big project I'm working on, but I thought I'd check with you just in case. Should Steve's task be taking priority over the project(s) I'm working on?"
In all likelihood your VP will hit the roof and either tell you to say "no" to the task, or (since it's the 2nd time this has happened) he'll speak to Steve himself. You can even go as far as telling Steve "why don't you just send VP an email, and CC me, and see if it's ok. Then I'll know right when you do!". I can bet that he'll try and avoid having an email sent.
If it were me, I would be trying Option 2 before going and speaking to the Mother Hen of the office, but try whichever is most comfortable first, let it play out, and see what happens before trying anything else.