In this paper, we propose secure relaying transmission protocols using rateless codes, where a source sends encoded packets to two intended destinations via help of intermediate relays. Employing nonorthogonal multiple access, two encoded packets can be sent to the destinations at the same time. In addition, two partial relay selection methods are studied to enhance reliability of the data transmission at the first and second hops. For protecting the source-relay and relay-destination transmission against an eavesdropper, cooperative jamming technique is employed. Particularly, in the first phase of each data transmission cycle, the remaining relays (except the selected relay) are used to transmit artificial noise on the eavesdropper, and cooperate with the selected relay to cancel interference components. In the second phase, trusted nodes that are near the destinations are employed to play a role as the cooperative jammers. For a fair performance comparison, we design a simple transmit power allocation for the transmitter and jammer nodes at the first and second phases. We also propose an adaptive power allocation method, where fractions of the transmit power are appropriately allocated to the signals, relying on instantaneous channel gains between the selected relay and the destinations. This paper also derives exact closed-form formulas of outage probability and intercept probability over Rayleigh fading channel. All the performance analysis is then validated by Monte-Carlo simulations. The obtained results clearly show a trade-off between security and reliability that can be enhanced by optimally designing the system parameters.