Can I withdraw 401K funds and invest them myself without penalty?

you can't....
after you pay your tax, you can invest your funds without penalty, visit myfxfunds.com for more info

No You can't. The following was taken from http://www.irs.gov/publications/p590/ch01.html#d0e1172 which describes all the requirements for an IRA. The import line for you in this case is:

The trustee or custodian must be a bank, a federally insured credit union, a savings and loan association, or an entity approved by the IRS to act as trustee or custodian.

There are three cases where I do not think it is wise to roll over your 401K.
The first case is when you leave your former employer after the age of 55 and are under the age of 59&1/2. If you meet this criteria you will not have to pay a 10% penalty from your 401K but will have to if you take money from an IRA. Once you reach 59&1/2 by all means roll it over.
The second case is where you have less than a thousand in your 401K and have no IRA anywhere else and your old employer will let you keep it in their plan without any fees. There are very few institutions which will accept less than one thousand dollars.
The last reason is that you know you do not have the will power not to do something unwise with the money. In a self directed IRA you can buy penny stocks, options, and host of high risk investments.
If you are like most people and do not fall into the above go to step two.

http://www.ehow.com/how_5608086_roll-over-ira.html

Yes, you can but there are restrictions. I would definitely talk to an Enrolled Agent or another tax professional BEFORE doing anything!

http://www.irs.gov/taxtopics/tc424.html

Only if you roll over your funds, but you might want to talk to a finance specialist:)