One thing about the Norse deities is They usually don't ask for more than you can give. They may give you certain tasks to do, but They know you can accomplish them. When They ask for certain offerings, it's the same way. The Gods know your situations (especially if They are regularly in your life), and don't ask for you to put yourself in the poor house over giving Them offerings. What They do ask if that you give what you can, when you can. This means that, if you can afford to give Odin a $100 bottle of mead, He would prefer you do that over a $5 beer. Not saying the beer wouldn't be accepted, just that the mead would please Him more. (Mead is one of His favorite drinks after all~) That said, if all you can afford is a $5 beer, then the Gods aren't going to turn you away or ignore you. I myself work on a very strict budget (currently unemployed and just made a major life move to another state), and have yet to have Odin tell me "no, that's not good enough." The trick really is to give what you can, when you can.
So, what constitutes good offerings for Odin?
As I’ve already mentioned, Mead! Odin loves Mead. Just about any alcoholic drink will do, but Mead would be His favorite. He is also pretty fond of whiskey.
Odin also seems to have a thing for crystals, when it comes to things I give Him. I was once perusing the crystal shelf at my local new age shop and He decided that Goldstone would be the perfect thing I should give Him that day. On His prayer beads, I also have Smokey Quartz, Citrine, and Amethyst. The latter two are two of my personal favorites as far as stones go, but when I was making the prayer beads, He directed me to the bin for those as well. Really when you think about it, they are great crystals for working with Odin. Citrine has an amazing energy and is quite inspiring; and Amethyst works great as a helper with meditation.
I’ve also lit candles and/or incense in His honor before when I couldn’t do much else, and at the time He was fine with that. For candles, I simply use the blue chime candles (with me He’s very big on blue). Incense varies, both by what I have on hand and on what He’s feeling on a particular day. Most often I use Lavender, though that could just be because that’s what I typically have on hand (that’s my favorite), but Frankincense and Sandalwood are also frequent offerings from me (in that order).
But more than anything, I have to say that He likes your time. Whether the time be spent on working on things He’s given you, or in meditation with Him. He also really likes it when you talk to Him. Sure, He can sit on Hlidskjalf and check up on things, but that’s not how you build a relationship with someone. You don’t visit your dad on the weekend, hand him a video and say “here dad, this is what I did this past week”. You sit and talk to him over a cup of Mead. Building a relationship with Odin (or any deity, for that matter) isn’t much different.