I believe anything given to you of significant value counts as taxable income, so I believe that the company taking taxes out of your check for the moving expenses is legitimate. I'm not sure though, so you may want to explain your situation to a tax professional and see what they say.
As far as 401k and IRAs go I should be able to be more helpful. 401ks are investment accounts that are provided through your employer, so your employer sets some rules that may be different from other 401k accounts. Usually though the only way to contribute to a 401k is to have them deduct money from your pay check; I have never heard of a 401k that lets you invest money from your savings and certainly not after the year is over. The contribution limit for 401ks last year was $17,000.
IRAs are different in that they are managed by you the individual, hence the Individual Retirement Account. You can set up any number of IRAs of any mixture of the types (Traditional and Roth are the two types of IRAs), but the total contribution that you can make between all of them was $5,000 in 1012 ($6,000 if you're over 50). Note that these are *Individual* retirement accounts, not joint or family, so that limit is a per-person limit. You as an individual must have made at least as much income as you put into an IRA for a given year, but if both you and your husband worked last year (and both made over $5,000) then you can both contribute $5,000 to your IRAs for a total of $10,000. You can make contributions to an IRA and count it as if it was made last year any time before April 15th. The company you set up your IRA through (I recommend Vanguard) will have an option for whether you want your contribution to count towards 2012 or 2013 when you contribute money. The limits on 401ks and IRAs are different and to not interact in any way.
Of the two types of IRAs, only Traditional IRAs would reduce your tax liability for a given year. In Traditional IRAs you contribute pre-tax money and then it is taxed when you withdraw it in retirement. So any money you contribute to a Traditional IRA you will subtract from your income before you calculate the amount of taxes owed. In a Roth IRA you contribute after-tax money, but then you owe no more taxes in retirement. (And in a regular investment account you contribute after-tax money *and* you will owe taxes on capital gains when you withdraw. IRAs essentially let you choose one or the other instead of both.) Traditional and Roth IRAs are mathematically equivalent if your tax rate now is the same as your tax rate in retirement. If your tax rate is less in retirement then Traditional is better, if it's more in retirement then a Roth is better. Most people will have a lower tax rate in retirement. You can contribute to both if you want to, but the total you contribute is what is limited and only contributions to the Traditional will reduce your current taxes.
To hopefully make this more clear let's do an example. Let's say that both you and your husband worked last year and each of you earned at least $5,000. You decide you want to invest in a Traditional IRA exclusively to reduce the number of taxes you will pay, so you open a Traditional IRA with Vanguard and contribute $5,000 (last year's max) to your account, marking the option that it should count as a 2012 contribution as you do so. Your husband decides he wants to hedge his bets because maybe tax rates will be higher in the future, so he opens both a Traditional IRA and a Roth IRA and contributes $2,500 to each of them (also reaching the limit), also earmarking the contributions as having been made in 2012. Your family can then deduct $7,500 from your income when doing your taxes. All of this is irrespective of and unrelated to anything else you might have done with a 401k.
Hopefully that is slightly more clear than mud, but don't feel bad if it's not. This stuff is pretty complicated.