No you can't move funds from a savings account into your 401k; that's a work based account that is controlled by your employer, and you have a cap of $18K per person per year, and the money usually is deducted from your paycheck (it isn't possible to my knowledge to do otherwise). If you want to max out the contributions, you'll need to double check how much you're allowed to put in, whether your company has a match and if it needs to be done over the course of the year or can you "front load" and use some of that cash you're sitting on to live off of for the first whatever months and max out the 401k contributions. Personally IMO, it's probably easier to just calculate the percentage/dollar amount by however many paychecks you get per year and set it up to come out evenly over the course of the year.
Each of you can fund an IRA (individual retirement account) up to $5,500 a year. There are two types of IRAs: Roth or traditional. Roth is funded with after tax income, traditional is tax deferred money (you would potentially get credit for using a traditional IRA account). You'd need to figure out which one makes the most sense for your income and eventual taxable brackets to know which type of IRA is best for your situation.
So that's a total of $11K for a married couple that can be placed into a tax deferred account type per year.
If you don't have access to an HSA (health savings account, can be used as a tax deferred holding account hybrid), then you are out of tax deferred options at this point.
After that, your only choice is going to be a taxable/brokerage account. This is an after tax account that can be opened anywhere, hold anything - stocks, bonds, mutual funds, etc - but needs to be more aware of any taxable stuff generated by the types of stocks and whatnot held since it can and will be subject to tax/cap gain/dividend rules and as such should be funded with things that will be tax efficient.
https://www.bogleheads.org/wiki/Principles_of_tax-efficient_fund_placementI just posted the following in another thread, and I think it might be helpful for you as well since it sounds like you're still at the very early stages of figuring out how all this stuff works. I knew nothing up until a few years ago, and found this forum and then Jim Collins and Bogleheads and this is my roadmap for how I got up to speed:
I read Jim Collins' stock series and it was like night and day - I literally went from scared and ignorant to excited and confident. Check out his site or get his book (based on the site). It is absolutely one of the best, easy to understand guides I've ever read.
http://jlcollinsnh.com/stock-series/Check out
Bogleheads site, but the following are the steps I took:
1. Wrote up an investment policy statement to figure out my goals and plans. This is my blueprint for what goes where, why I do A or B if this or that happens, where I want to go in the future, and how I'm going to get there.
https://www.bogleheads.org/wiki/Investment_policy_statement2. Figured out my asset allocation (AA). This is based off of how much risk/volatility I felt comfortable with and set up my portfolio to reflect my AA (which would also include any real estate).
https://www.bogleheads.org/wiki/Asset_allocation 3. I then took a look at what I held where, sold off everything that didn't match up with my goals in my IPS (I decided I was going to be an index investor holding only 2-4 total mutual funds across my entire portfolio, YMMV). I built a lazy portfolio and I am quite pleased with the ease and elegance of it all.
https://www.bogleheads.org/wiki/How_to_build_a_lazy_portfolio