Georgia is not part of the Schengen area, however it does have special rules for valid Schengen visa holders. According to the Georgian ministry of foreign affairs:
Foreign nationals who have a multiple entry US, EU or Schengen member
states visas, which have validity for one year or more and had been
used once at least, can enter or stay on the territory of Georgia
without visa up to 90 days, within the validity term of the visa.
Therefore you will not need a visa to enter Georgia in the circumstances you describe.
Turkey is also not part of the Schengen area and will require you to get a visa to enter its territory. According to the, the rules for Indian passport holders are:
India: Diplomatic passport holders are exempt from visa for their travels to Turkey up to 90 days. Ordinary, Special and Service
passport holders are required to have visa to enter Turkey. Ordinary,
Special and Service passport holders with a valid Schengen or OECD
member's visa or residence permit may get their single entry e-Visas
valid for one month via the website www.evisa.gov.tr, provided that
they meet certain conditions.
That is, you definitely will need a visa regardless of whatever other visas you have, however you may be able to get an e-visa online. Failing that, you can always get the visa at the airport on arrival. If you are entering Turkey by means other than air (e.g. by road from Georgia), then you will need to get a visa prior to your travel.
Czech Republic, on the other hand, is a member of Schengen area and a valid Schengen visa is required to enter Czech Republic. As you already have one, you should be ok - provided that it was either issued by Czech Republic in the first place or you have already entered Schengen area in the past using this visa or are transiting through Czech Republic to the country that issued the visa.
EDIT: Where you are travelling from makes no difference on the admission policy in any country (with possibly some very rare exceptions, like Israel to Syria, for example). What matters is your country of citizenship and the type of visa or visas you hold.