Can my parents transfer money, stocks and IRA's to myself that medicare cannot take?

The "look back"; gifting and the rules are VERY complicated, and require the assistance of an elder law attorney to detailed, fact specific answers.
The first link I provide here, answers most of the questions you have , up unitl what property can go to whom, and when. What many people do ( and I not advising this) howvere sinec the home is exempt, put all their resources ino that and then put the home in a trust. But you need an expereinced attorney to details out your assests and future.

http://www.theeldercarelawfirm.com/PracticeAreas/Medicaid-Myths.asp

http://www.edlc.com/PracticeAreas/Medicaid-Eligibility.asp

http://www.elderlawanswers.com/

http://www.ozarkselderlaw.com/page.php?id=2

Medicaid laws can be very confusing, however the state can put a lien on the patients home, if the person is on medicare and medicaid and a resident in a nursing home. The patient has to of had another persons name on the home within a five year period before residing in the nursing home before the state can not put a lien on the home.Also when a person needs medicard in a nursing home, DSS can look back over the past thirty six (36) months to see whether you intentionally gave away money or property to become eligible for medicaid under the new law (The DRA) starting February 8,2009, the look back period will increase each month until it reaches 60 months on February 2011. For additional information on laws you can call the statewide legal service at 1 (800) 453-3320