Connect it up:-
e (emitter) to GND
c (collector) to a digital input pin. Then that pin to 10K resistor to +5V.

c (cathode) to GND
A (anode) to a 150R resistor, other end of resistor to +5V

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No it hurts the sensors.

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That is a collection of words that make no sense.

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Well
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So you connected an LED across the supply and it still works. Sorry no you didn't. (see point below)

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I do realize that English is not your first language but connecting things to +5 and GND is not connecting them to the arduino it is connecting them to the power supply. I am sure you don't mean this but I don't know what you mean.    

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I am looking at the data sheet now and this sensor has four wires not three. Are you sure you have the TCRT5000L? It says:-
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Now if you have a sensor with three wires with one connected to +5V and GND then you have not got the Vishay Semiconductors TCRT500L. So that being said let me consider the rest of your question.

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Yes that will be ok.

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If you connect each DATA line to a separate digital input that will be fine.
If you want to connect all 4 sensors to 1 input then there will be problems. As you don't have the device you think you have, or at least the data sheet I am looking at I can't say how you could connect them up. Assuming it would not harm the sensor it will act like a "wired OR". That means if any one sensor is receiving a reflection you will not be able to say what the other sensors are doing.

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If you have the 4 wire sensor I am looking at then yes you need a resistor in series with the LED. The data sheet has this photo:-



The LED can take up to 60mA so a small resistor will be OK. If you feed it with 5V, you get about 2 volts across the diode and so the resistor has 3 volts across it. So with E=IR for a current of say 40mA you need a resistor of 3/40 = 75 ohms.
However as you have a 3 wire sensor I don't know what you need.

Right that explains things.

You have a board that contains a TCRT5000L sensor built on it. Not the TCRT5000L sensor itself. If you look at the schematic of this board you will see the sensor surrounded by dotted lines, that is the TCRT5000L sensor.

It also has the resistors connected on this board so there is no need to add your own and you can connect it like you want without any harm.

I would have designed this board differently, by putting the resistor in the collector not the emitter. If you put it in the collector you get the amplification factor of the transistor, if you put it in the base you don't.