Does the driving on overdrive mode cause high fuel consumption, because the transmission use the first three ratios mostly?

the over drive is controlled by a servo/solenoid that sometimes fails
It could be a TCM problem
It is not an indication of a failing transmission unless you have more indications you have not mentioned and if diagnosed by an accredited transmission shop should be fairly cheap to fix.
It is worth fixing

I have never known an overdrive that cannot be switched on or off at will or engaged or disengaged.

There are two definitions of overdrive and in the philosophy of some people the fifth gear is an overdrive.
The conventional manual gearbox, because the first motion shaft is locked to the third motion shaft in the top gear ratio, any supplemental ratio that has a ratio higher than 1:1 is considered an overdrive ratio.

The more traditional definition of an overdrive is a supplementary gearbox that can be incorporated into a normal manual gearbox to provide a single overdrive ratio for the purpose of quieter and more economical cruising.
The early overdrive was cable operated by a large chrome-plated dashboard-mounted handle. Later overdrives were hydraulic units that could be switched in or out by electricity, often by the means of a steering column-mounted switch or by a tiny switch incorporated into the gearknob.

A typical installation included an inhibitor switch mounted on the gearbox which prevented overdrive operation in the lower ratios when the benefits would be dubious.
Sometimes a lower than standard final drive ratio would be used and the overdrive ratios which typically could be selected whenever third or fourth gear was selected could be used together to produce something like a six speed close ratio gearbox which was hitherto unheard of when some of the rest of the world was still using "three on the tree" type three-speed gearboxes.

Most manufacturers had dispensed with overdrives by the end of the 1970's due to the weight and added expense, in favour of the now common five-speed gearbox, though Nissan incorporated an overdrive ratio into their automatic transmissions to compensate for torque converter slip when fuel costs began to rise disproportionately.

If you have an overdrive unit fitted to your car that doesn't work, I advise starting the diagnostic process by checking through the electric circuitry, wiring, switches and solenoid.

Driving in overdrive, say on a trip where your speeds are over 65 to 70..Actually saves gas, but using overdrive to drive around town not only uses more gas, but can cause damage to your transmission.

The size of the crown wheel gear. Ford 9 inch is a strong diff used in V8 models. The 8.8 is slightly smaller but is still a good diff. The gear ratios will probably be different. Manual gearbox cars have different ratios to automatics. The higher the ratio, the faster takeoff you will have but lower terminal speed. At high speeds , the high ratio differential will cause high engine revs and poor fuel consumption. A low ratio will be mediocre takeoff but allows high top speeds and lower engine revs. (Good for fuel economy if you are mostly highway driving)

Sounds like your transmission or lockup converter is slipping. The slipping causes heat and it is downshifting out of overdrive as a built-in protection strategy. Get the transmission looked at ASAP before you get stranded because it's stuck in a downward spiral right now. The problem could be caused by a stuck solenoid, which is a relatively cheap fix, but the more you drive it like this, the more you're working toward a full, expensive rebuild.

hi
the first thing i can suggest is map sensor this controls the air to fuel ratio in the vehicle most likely soulution to the problem you can go down to any auto parts store and they will 9 times out of 10 have it in stock any other questions please feel free to ask again thank you

This is a very wide encompassing question. It basically revolves around a thorough engine diagnostics and tune up, replacing filters and plugs etc. The quality of all oils will have a small influence on fuel consumption, as will type of tyres and tyre pressures. The most profound influence on fuel consumption is however your driving style and that is a subject too vast to go into here. It boils down to a smooth driving style, judicious use of the transmission (manual or automatic) and driving within the engine torque range whenever possible. Finally high speed requires additional fuel to deliver the power it needs to overcome wind and rolling resistances.

No not at all, i fact it is quiet handy and should be used in ost driving situations. o/d stands for overdrive. When you select this mode the transmission goes into overdrive. Someing up in a sentance, the engine is required to do less revolutions to turn the rear wheels through different ratio's. Most times overdrive wont kick in until around 45mph. Use this function at all times and you will get better fuel economy and put less strain on the engine. Turn it off when towing or approaching a big hill!

sounds like the vac control valve or the kick start cable is fitted right ,but then you did have the rolls royce of auto boxes in as original ,a c4 which should be about 3000rpm for 70mph ,depending on the final drive ratio fitted to your car

Do you remember by chance speed vs RPM before & after work done? for example : before was 2000 RPM @ 60 MPH. Now 2200 RPM @ 60MPH ? May be coincidence, and transmission not shifting to overdrive or high gear.